This is actually a confusing issue because the DLC expansions wildly change the mechanics for Terra Incognita, and there is very little documentation about this on the wiki.
'Vanilla' EU4 Terra Incognita Discovery Mechanics
In 'vanilla' EU4, you discover new ocean provinces by moving a fleet with an Explorer on to the unknown ocean tiles. You also randomly reveal coastal land tiles when you move into an adjacent ocean province. To normally reveal land tiles, use an army with a Conquistador. An army with an a Conquistador can also directly disembark from a fleet containing transport ships to a coastal province with Terra Incognita.
DLC Expansion EU4 Terra Incognita Discovery Mechanics
If you have certain expansions enabled (El Dorado), the mechanics are almost completely different. Explorers can no longer move into Terra Incognita tiles at all. Instead, any group of 3 or more Light Ships or Transports will have a "Send Explorer" option which shows you a list of possible 'Exploration Missions'.
There are two different types of Exploration Missions. One is "Explore the waters of X", which sends the fleet out to systematically reveal ALL ocean provinces in the 'X' region. The second type of mission is only available after the first Exploration Mission is completed (or partially completed), and it is "Explore the coast of X", which sends the fleet out to systematically reveal ALL coastal provinces in the 'X' region. Which missions are available to you depends on your Colonial Range from one of your provinces to the region in question. You need a certain range to enable the first mission and a bit higher range to enable the second type of mission.
Comparisons and Conclusions
There are pros and cons to each approach. With vanilla mechanics, there is no limit to how far you could reveal Terra Incognita. You could take your very first fleet directly from Japan to Africa and disembark and conquer the Kongo. With the DLC expansion mechanics, this is impossible. However, you suffer no naval attrition damage when on an Exploration Mission. Some missions, like "Explore the waters of Australia" or "Explore the waters of Oceania" would take many, many trips for an Explorer to complete without the DLC expansion mechanics enabled. Additionally, unless you are using the disembark method, it can sometimes be hard to reveal the coastal land province you want using the vanilla mechanics, since the provinces you reveal are completely random (and not remotely comprehensive).
In my opinion, neither version is superior. I play with the DLC expansions enabled because the other mechanics they provide are excellent. However, if you were trying to do some very specific early exploring (for the purposes of pure conquest), I could see how the Exploration Mission mechanics would be limiting, since they are based on the premise that you would want to colonize the regions in question.
A Note About Full World Exploration
Note that there is no way (with either mechanic) to reliably discover uninhabitable land patches of Terra Incognita. You have a chance to discover them over time if you have a province near the area (or an ally does), but it's pure luck. It makes getting the World Exploration achievement annoying when you have 99.9% of the world explored and are only missing a patch of uninhabitable land in Siberia.
I'm afraid all old saves previous to the 1.12 patch (which will be released in line with the Common Sense DLC) will be broken and unplayable.
Apparently this patch will be quite a large overhaul. To play you're old saved games you're probably going to have to elect to run EU4 in a previous version within Steam. Or set it to not Auto update.
But then because you're running in an older version all the nice new features in the new Dlc will be unavailable to you.
See this Reddit post
Usually the act of enabling a Dlc will not disable an Iron Man save. However the larger Dlc's are usually released along side large patches. It's the act of upgrading to these new patches which can and often do break old saves. Dlc's which have already been released and minor Dlc's such as music / flag / graphics packs aren't an issue.
However as a side note the use of certain Dlc's are known make Iron Man mode saves ineligible for steam achievements. Such as character designer in Crusader Kings 2.
Best Answer
As @Clyde as already pointed, it's just a game mechanic that is unavoidable and pointed out here http://www.eu4wiki.com/Ruler#Deaths
If you don't have any good modifiers for stability cost then I'd avoid using your ruler (or heir) as a general, unless they're terrible, like Castille's starting ruler and heir.
A further piece of advice is to get a stability cost modifier. My usual go to for this is under religious ideas(http://www.eu4wiki.com/Idea_groups#Religious) as Church Attendance Day.
If you want to avoid this entirely, switch to a republic. They won't suffer the stability hit and you'll also always get a leader with average stats(e.g. 1/4/1). There are events for switching for certain nations or you can let legitimacy fall low enough to spawn rebels.