Do abilities that trigger when a card is turned face up trigger when that card is in exile?
No, the turned face up ability does not trigger when the card is in the exile zone. Rule 112.6 says


  Abilities of an instant or sorcery spell usually function only while that object is on the stack. Abilities of all other objects usually function only while that object is on the battlefield.


This ability does not match any of the exceptions, so it does not function when the creature is not on the battlefield.