The GM takes on more work than any individual player in making the world and the game come to life. Obviously a GM without players has nothing, but the lynchpin of the game is still the GM. Having played in many games and GMed many more, I come into any game with the understanding that because the GM has to do so much work just to get the game going, that person should be given the benefit of the doubt where possible.
Your player's reaction to me seems a bit off, in that you were just getting back into GMing and this was the first session in a new campaign. To expect everyone's expectations to align perfectly, and the session to play out without corrections or adjustment is asking quite a lot.
For detailed background, I generally provide overview text and invite the players to ask questions as they come up. It's perfectly acceptable for a player to say, "I figure these thugs should be licking my boots because I'm a member of the guard. Is that right?" This approach requires that the GM be able to fill in details on the fly, but it also puts some of the responsibility on the players. Some players may bristle at this approach because they find it too meta, but the necessity of using it fades away as the campaign develops and the players become more immersed in the world.
Different players get different things out of gaming. Unfortunately, some people's gaming styles mean that their fun comes at the expense of others'.
Often in a case like this, the player either wants more attention than the other players or, via their outlier character, wants their character to constrain/implicitly control the rest of the group. This is unhealthy and distracting to the rest of the group, and they are justified in not liking it.
First, forward the group Making the Tough Decisions (see the "Deciding to React Differently" section) and ask them to read it. "My character would do that" is not an excuse for being a jerk. They need to find a type of character that provides their kind of fun but not at the expense of the experience of the other gamers. I had a player once who wanted to be "evil" and work against the party, so I had him be a spy and send reports back on their activity all the time, but was strictly instructed to "never blow his cover." So to the rest of the group he was perfectly helpful. The player eventually left and the PCs even still kept up with the NPC, they never found out he was a spy. This got that player his somewhat-dysfunctional fun without adverse effect on the group.
Second, the other players don't have to accept the control of the outlier character. Make it clear "we don't want that." If they do it anyway, then just have your characters react as they would in game to a weirdo freak. We had one serious game, with espionage and such, and a player brought in a new gnome character who was clinically insane. He'd just say stuff like "Turnips wheee!" and not make any sense. When he found out our secret-agent stuff, we sat him down and said "So, can you keep our secret?" "Turnips wheee!" "OK, so listen to me very carefully. If you don't start making some Goddamned sense right now we're going to tie you in a sack and drown you in the river." Our characters were not willing to have their lives in the hands of some incoherent freak.
This may lead to group exclusion. Which is sad but sometimes you have to do it. We had one player that was always "like that," and when he brought in a new character to our sci-fi game it was the last straw. Our spaceship touched down, we went recruiting crew. This guy couldn't even express why we'd hire him. "I have... skills. I can do things... that need doing." We left him on the planet. The group met later and decided to disinvite him from the group, as he just did that all the time.
@JonathanHobbs cites the Five Geek Social Fallacies, and he's right to do so. Heck, there's two of them, let them go play their own freak game together. Because groups have a right to set their playstyle. It's like recreational sports teams. Some people want to be goons and dress up in mascot costumes and play silly soccer. Other teams want to be serious and compete. Both get something different out of the hobby. But the serious team is welcome and expected to bounce a "mascot boy" from their team.
And third, we come to splitting the party. I was running games for a fairly large group, and I and some of the players wanted to do a more seriously immersive game. Half the group was on board and half wasn't. So I started an immersive game and invited those people to it, and I started a "fun" game and invited the others (eventually rotating out of GMing for the "fun" one). We had a five year long super deep immersive campaign that everyone looks back on, ten years later, as our single best roleplaying experience ever. You deserve that, and you don't have to always give in to someone that doesn't want that.
Best Answer
I know of two approaches to resolving this issue.
Give everyone the experience: Instead of giving a player XP if they write a summary, give every player XP for each player that writes a summary. This keeps the footing level for all the characters, but also encourages players to write summaries (and to harass the rest of the party about writing summaries). You might even give an additional bonus to the party if all of them write summaries (something more special than yet another dollop of XP would probably work best).
Give some other reward: The problem with experience is that, like DDT in fish & birds, it accumulates over time. You could instead offer some kind of reward that doesn't accumulate in the same way. You might offer action points (in a system that supports them), or "plot coupons" which allow their bearer to dictate one non-trivial aspect of the story (as long as it doesn't ruin stuff). You might even (depending on group dynamics; this would be a huge no-no for some groups) raffle off an exemption to contributing to snacks/drinks at the next session among those who write a summary.
Note that you can also combine the two approaches. When a player writes a summary, give the whole group some XP, but also give some other reward to that specific player. This combines the group-wide incentives of option 1 with the earned rewards of option 2.