Yes Ceridan, correct. The two effects are simultaneous, hence it's a First Player's decision
Posted 14 December 2013 - 06:51 PM
Well the FAQ only splits hairs by saying that if you're drawing Mythos cards and using the gate location for some effect, only the top location is used. This would very loosely imply that during a normal Mythos phase, the top gate should be resolved first, which would (in your case) cause you to win the game.
Again, loose implication only.