Yep! The adversary can start anywhere they want (on the mini-map, of course), as explained in each adversary's "Setup" section in the Adversary rulebook. This may change with future adversaries, but the current adversaries have no restrictions on their starting locations.
Where exactly does the adversary start? Can I freely choose the position?
Yep! The adversary can start anywhere they want (on the mini-map, of course), as explained in each adversary's "Setup" section in the Adversary rulebook. This may change with future adversaries, but the current adversaries have no restrictions on their starting locations.