In the Dunland Trap, some card, including Dunlending Ambush, make search an enemy in the encounter deck and "put it into play engaged with a player".
Does it trigger the Chief Turch forced effect which reads
QuoteAfter an enemy engages a player, remove 1 time counter from the current quest.
I am sure you guys have encountered this situation in the past. With my 2 solo games, it already happened several times (an I guess it happens even more in multiplayer).