I have no official confirmation on this, but my guess is you only resolve effects on cards that are "in play". Since you are only choosing which will become the active quest, I reckon none of them are "in play" until you choose one.
I'd be calling it that the "When Revealed" only occurs when the quest becomes the active quest, as there can be only one active quest. As you're only choosing one of them to become the active quest, only that one will then activate their "When Revealed" (per the "Reveal" trigger on Hasty Council). Which is probably also the common sense answer as to how it should play.