In the "Beyond the Gates of Hell" scenario, if all of your heroes are standing in the six highlighted spaces of the gates of hell, you accomplish the quest.
Can you immediately accomplish this quest when you rest and resurrect your heroes and they are all in the six highlighted spaces ? In other words, when can you accomplish a quest? Do you have to activate a hero to accomplish a quest? Can a quest be accomplished out of your turn?
Never played the quest, And i don't know the exact rule here but I would think you could accomplish it by resting if there is no special rules for the tiles (like must spend a movement or to enter).
I would say also you are not "out of turn" since resting is your turn.