You may only leave Manhattan after being attacked with a dice roll from another monster. You have the choice of leaving Manhattan immediately after deducting your life points.
Receiving damage from units or card effects doesn't count as an attack and therefore doesn't give you the choice of leaving Manhattan.
You may also use the Subway card to move out of Manhattan at ANY point of your extra turn.
"Heal 2 damage and take another turn. During this extra turn, you can move as often as you like, whenever you like."