by dougtempel
It's explained on p. 24 of the rulebook. The treachery card effects are resolved (or canceled by a response, such as A Test of Will or Eleanor). Once the treachery is resolved (p. 24, "Once all encounter cards attached to a guarded objective are dealt with..."), then the objective is available to be claimed per the instructions on the objective card.Surge or Doomed keywords on the treachery card should also be resolved, so additional cards would be revealed and placed in the staging area (Surge), or each player's threat would be increased (Doomed). That's in section 1.01 of the FAQ (v 1.3).
The heroes are in play and could be affected, but often you'll catch a lucky break (e.g., The Necromancer's Reach wouldn't damage any characters because none are exhausted at that point).