But this was BEFORE my actual turn. I thought there was some kind of "reset" after an additional turn once I make my next regular one... And sure, if one plays an Outpost during a Possession turn, the possessed player draws only 3 cards, but those additional turns are connected. In my example those were two seperate things... but obviously I was wrong about this
Outpost says it can't make you take more than 2 turns in a row. Your Possessed turn is one of your turns. And your regular turn is a second turn in a row for you. So Outpost can't make you have a third consecutive turn. I believe this case is covered in the Possession FAQ in the rulebook.
Possession + Outpost makes for some of the most confusing and subtle card interactions in the game. One of the weirdest things that can happen (though I don't think it's implemented on isotropic) is if I play Possession twice on my turn, then make you play Outpost on the first Possession turn: after you draw the 3 cards during cleanup, I get to decide whether you play the Outpost turn or the 2nd Possessed turn next. Drew 3 Estates? No problem, I can let you control that 3-Estate hand (Outpost turn), then go back to Possessing your next 5-card hand. Or I can look at those 3 cards and decide I'd like to Possess them after all (instead of letting you play your Outpost turn first), and then the Outpost turn never happens and you get your regular turn with 5 cards.
edit: Removed a bunch of stuff that is highly questionable since it contradicts specific instructions in the rulebook (even though Donald's timing rulings on BGG seem to contradict the rulebook). If you're interested in subtle questions of Possession/Outpost timing check out this thread on BGG:
http://www.boardgamegeek.com/thread/662495/outpost-and-possession