Villians are particularly nasty because they activate regardless of who's turn they activated on. I know monster groups that are activated by certain players would activate only if someone else had a similar one, but villians care not.
does it switch to the 'control' of the active hero every turn?
The active player controls the Villain.
At the bottom of the Villain card, it should say something along the lines that the Villain is past to the next player. Therefore the Villain is activated on every turn and is controlled by the active player.