Rulebook is a little nebulous about the timing. I declare a Water conflict that ends up being against Elemental Fury province. Does Adept of the Waves' Covert get to trigger? Or does my opponent get to change the element type first?

Rules Reference page 21

Quote

Declare which ready characters (under his or her control) are being committed as attackers. The attacking player may declare any number of eligible characters under his or her control as attackers. Slide these characters toward the center of the play area, away from the attacking player’s home area. At least one character must be declared as an attacker at this time in order to initiate a conflict. If any of the attackers have the covert keyword, the targets for covert are chosen at this time.

Each of the above items are considered to be performed simultaneously. If any of the above cannot be completed, the conflict cannot be initiated.

If the province being attacked is facedown, turn it faceup as soon as a conflict is successfully declared against it. This occurs before any reactions to the process of conflict declaration may be triggered.

Judging by this I would say you get covert before the province is revealed - the province is still face down - when you reveal it, its reaction to being revealed is too late to stop Covert from taking effect. It has already been activated and assigned, so I don't think losing covert would retract the already-resolved aspect of the keyword.

Thank you for clarifying. The Learn to Play says a lot happens simultaneously, and doesn't mention anything about the successful declaration bit.