When using the arsonist against the Hedge Tavern, where does the Hedge Tavern card go? Does it go to the bottom of an "Era of Turmoil" stack or does it go back to its original starting position face up?
I would play as per the wording on the Arsonist card. Just because the Hedge Tavern has an unusual starting placement, in a face-up stack, doesn't mean it should be exempted from subsequent effects.
Given that there is an stack available with the same back as the Hedge Tavern, I see no reason why you shouldn't follow the course of action prescribed by the Arsonist card, and put the Hedge Tavern to the bottom of such a stack of the opponent's choice.