The trigger occurs when you use the Morph ability to turn the card face up, or when an effect turns it face up. It will not trigger on being revealed or on leaving the battlefield.
Morph (You may cast this card face down as a 2/2 creature for . Turn it face up any time for its morph cost.)
When this creature is turned face up, regenerate target creature.
(You may cast this card face down as a 2/2 creature for 
. Turn it face up any time for its morph cost.)