Good question! It's a little of both, really.
Recalling the quest tends to be a fairly collaborative part of the game, especially for the Heroes. But like a GM, the Evil Player is allowed to make "hard moves" such that they have "final say" over how an Event the Evil Player recalls plays out.
During the Final Fight, the Evil Player is definitely taking on more of a GM role by playing an antagonist.
(Not sure if this explanation helps at all 😅)