One of the problems that I run into with Fate is the preconceived notions of what a GM is, and the role played in other games. Fate is about the story, more than the system, i.e. the story utilizes the system rather than being constrained by it. So, though it may seem that you are letting the players know about something that they do not, what you are really doing is introducing a story point to move things along.
In the best instances of synergy, his utilization of the aspect would involve revealing it if it affected some roll that involved the player. But, just because this is not the case doesn't mean that the characters know- just the players.
This does not mean that the player can't invoke it by spending a fate point, but it does mean that the invocation does have to be explained in such a way that it would not rely on the character's knowledge. An example of this might be the player spending a fate point to hinder the other character because of the fact that he is an undercover police detective, and this fact constrains him, rather than the player.
I've found that though details may be hidden outside of interaction with the player, once the players become involved, its not so much hiding details, as to how they interact with the story.
Also see this thread where I pose a similar question- like I said, I had a hard time getting past this.
One last point- the reason that the players need to know is stated in that other thread- since the players can spend fate points to alter the results of the roll, they need to know their target.
That said, if you do want to have aspects that are hidden to the players, I'd say that there are a couple of ways to do it- and a couple of caveats that you have to watch out for.
You can use tangential aspects to the primary aspect to act as breadcrumbs towards puzzling out the primary aspect. I've done this in my game. But the caveat is that you can't be too obscure in your placement, so that players can actually puzzle out that their is more to the situation than meets the eye. If you are too clever, then you can find yourself in the unenviable position of having to try to figure out ways to drop hints so that your players can find out your big reveal.
An example of how I've used this:
There was a person of note in the campaign that was seemingly a villain, but was actually a patsy and a victim; their bodyguard was the real threat in the scene.
The patsy had the aspects Detached to a fault, Listens to his subordinates, and Winning is everything. These covered that he was Addicted to Red Court Venom.
The bodyguard had the aspects Divided Loyalty, Has his boss' ear, and Strong as an Ox to imply that he was Red Court Infected.
The aspects that told the story were there, and as the players saw clues, they were able to puzzle out the mystery. But it was harder than it needed to be, as though the aspects seemed obvious to me, they weren't obvious to the players.
Always keep that in mind, and have a definite plan for the reveal that doesn't necessarily involve the players' agency.
As I looked back on it, I saw that last caveat as the reason that I would use this sparingly, and concentrate more on the story than the plot points and being the GM. Player agency is important in Fate, and to an extent, this removes that if they don't follow your orchestrated plot.
This always seems to be the answer, but...
Talk to the player first.
I'm assuming you have some means of contacting your players outside your normal game time, if only to set up game or let each other know of cancellations or emergencies. Send your player a message, something along the lines of "Hey, I've noticed that you seem dissatisfied at game lately. Is there something going on you're not happy with? I want to make sure our game is fun for all of us, so please let me know if you have any concerns."
See how he responds to that. If he responds with a list of concerns, use those as a starting point. If they're things you can address, try to do so. If you think his problems are irreconcilable with your game and/or the other players, then say that, politely, and suggest that he might want to look for a different game to join.
If his response is neutral or brushes you off (such as "nothing's wrong, see you next game"), then you can let it go for a session or two. See how he behaves, and whether he raises the issue himself.
Ask another player to initiate communication
If you're not comfortable approaching the problem player directly (or don't have the means to do so), you can speak again with the person who told you this player wants to leave. It sounds like the go-between is friendly with him, so you can ask the go-between to, next time the player brings up the issue of wanting to leave the campaign, tell him to talk to you about it.
Don't use the go-between to actually convey messages like "I heard you want to leave, what did I do wrong?". That kind of thing usually gets lost in communication, and it puts the second player in an awkward spot. Just ask him to pass on that you're open to hearing your players' concerns and that the player is welcome to talk to you if he has a problem.
Don't jump the gun
Either way, don't rely on hearsay to drop a character and his player from the party. Don't allow the other players to sacrifice this guy's character unless you have his explicit buy-in (or if it comes up naturally in-game and the player himself is all for it). Don't assume that he meant what he said about wanting to drop, either - I've had players complain about my game in moments of frustration, but when I ask them if there's something I can do better, they reassure me they're having fun and were just briefly frustrated.
TL;DR: Communication is your friend!
Talk to the player. Follow his lead, and don't make assumptions based on what other people are telling you. If you handle this issue with grace and good will, then it's highly unlikely the other players will see a reason to stop playing a game they enjoy just because their friend did.
Best Answer
To me it sounds like your player is a mix of being impulsive and a newbie to roleplaying. The newbie elements (needing stuff explicitly explained and such) should work themselves out with time. The impulsiveness usually needs a little bit of work.
Here's what I did once to rebuff the impulsive players in my campaign:
I did this to deal with a combat monster who kept doing stupid things (shooting up places, making a "peace gesture" that got the party shot at, and spooking an extraction target [leading to his death]), and it worked pretty well- he was the face of the group, and decided that when the "nanite antidote" that was supposed to cure the party's impending doom nanite fun death he would drink the whole thing to ensure he didn't die (because only two party members were actually really in danger of death, him being one). Turns out that there were no nanites, and the antidote was cyanide.
That was the opposite of what I should have done.
Mind you, it didn't destroy my group, the player stopped being impulsive, and life went on (for all but that one guy's character). But it was a stupid, brash, inexperienced GM maneuver, and it could've cost me a player. It did have the upside of making everyone else more paranoid, but the impulsive people are still impulsive, they just put a layer of paranoia on their actions (which I guess makes them less impulsive by definition, but doesn't promote good decision making).
Ultimately, you will run into these brash and (frankly) obnoxious players. It's not even a personal fault in them; the three or so I have/had (as their various states of rehabilitation qualify them) in my group are all really nice guys, but they just don't create a coherent character. So here's what I've started to do with them:
Disclaimer: You may have other factors leading to this issue.
Wrong Game: The player isn't actually interested in playing this game; even if they're interested in the setting and mechanics, they don't want to abide by them. This is what I call the "Sparkle Vampire" syndrome I occasionally have to deal with from a player who read all the supplements and got a bunch of ideas ("But the book says cyberzombies are only really, really, really hard to create!) that they then assumed would apply to their characters. These are the sort of people who want to play sentient variants of high-level D&D Monster Manual entries, fully sapient human-form mind animals, and the like. If they were playing Eclipse Phase they'd go for the Octomorph and give it a fancy cybernetic suite including jet thrusters.
Bad Player: I hesitate to call someone a "Bad Player", but it's true that some people prefer to play things revolving around them. While this is natural, some people take this to an additional extreme, and must make everything they play revolve around them all the time. Sometimes this leads to "The Talk" (see above), and sometimes this just means they won't have fun in the game and should pursue something else.
GM Ineptitude: Note that I'm not accusing you here, and I'll keep the examples my own. I used to run an Eclipse Phase game, and I made the players into hard hitting immortal cyborg soldiers. It lasted three runs. My players got bored because they had no consequences for failure. I ran a Remnants game. It failed because the players kept running into issues where their (overly large) group kept falling apart on matters of dogma or running into massively high power gradients. This same group has been in a Shadowrun campaign that lasted for almost a third of a year with weekly sessions, and the reason it ended was due to scheduling conflicts and getting far outside the realm of mortal power. It's not that this even means I'm a bad GM, it just meant that I was aiming for something and my players weren't, and there was a communication breakdown or I tried to push it on them too hard (or I over-hyped them).