Betrayal at the house on the hill movements/attacks
Monsters never automatically attack; they only attack based on the haunt-specific rules that traitor has. It’s possible for a specific haunt to have a rule such as what you are asking about, but it is a turn-based game; and normally characters only get to act on their own turn.
Since you brought up how it works thematically (it is a game based on theme after all), the -1 movement when you leave a room with a monster kind of explains it... think of it as moving extra slowly and spending time going the long way around the room in order to avoid the monster and sneak by it.