When some card effect read "reveal cards from encuounter deck" or "reveal encounter card" in any phase of a round (may or may not be in quest phase). Do encounter keywords (when reveal, surge, doom etc) revealed by this way alway trigger in the phase?

How can I resolve a card effect or a key word (such as the Burgle) read "reveal cards from player deck"?

Revealed card from the encounter deck are adding to the staging area (or resolved and discarded for treachery). Whenever.

Keywords are shortcut. If the keyword referes to «when revealed» then do it. In any case, look how the keyword's full text is worded to find out.

Revealed card from the player deck are revealed. You just look at them and put them back. That's all.