Hmmm... I wonder if that's because evil Kirk was evil and therefore it's okay to bring regular Kirk back.
In that case, Kirk needed
to be integrated, because "good Kirk" was incapable of being a captain - without his dark side, as it were, he couldn't exercise command decisions. Also, "evil Kirk" was an evident threat to the ship. So those two things make it more obvious in Kirk's case than in Tuvix's.