by sigmazero13
Quests can only be resolved during the Quest phase, and only if you chose the "Move" option.There are only 2 exceptions:
1) The "For Terrinoth" Quest is resolved during a battle in a hero's area, outside of the quest phase.
2) The "Hired Sword" Quest can be completed if an enemy hero attacks you during the Quest Phase, even if you didn't chose the Move option. However, note that a hero can only do one quest during the Quest phase, so if your hero already did a quest that phase, he can't do Hired Sword, and if he does Hired Sword but gets a chance to move later, he can't do another quest.
Both of these quests are from the expansion. All "travel" quests require you to be in the specified area during that hero's activation during the quest phase.