The game may be going with the theory that there are a multitude of timelines where various things happened. All the Exarch did was come back and intervened, causing the game's events to branch off into a new direction. It won't effect his timeline, that one is done and can't be reset. This can explain why he's still here, why the Crystarium is still here, and how they can basically wrap up the time travel hijinks without going into full on confusing time/space rules. Because time travel can REALLY get confusing otherwise.