Are you referring to the "bonus" that comes with your specific choice of deity when you first create you character?
'cause if you are then, "no", it has nothing to do with time. So far, I've only seen it activated just before Leves. I think you can manually activate it from Aethyrite-thingys at any time, too, but I have yet to. I don't know what it does, or what the different guardians' bonuses are, but I know they cost 10 favor points, and I think my max is 200.