I have notice the same problem. The ships of a faction that are taken over with influence are not turned into pirates but are still a live faction that you can trade with, which is how I think its supposed to be. I actually gifted a fleet with transports to a faction like this so they could take a planet from another AI to get back in the game.
The main issue is, as you say, that if they are not at war they dont move there ships off your planet. I assuming since the AI has no reason for them to go anywhere they just sit around. If you really wanna move them you can gift them a few ships/transports so they can go to war or you can turn on god mode and move them yourself.
That being said, probably worth making a ticket for it.