(Sorry for replying a month later; just now poking around for rules clarifications & saw the question.)
Luckily, this is actually explicitly answered in the FAQs:
What if I'm in battle and both my enemy and I compromise to end battle? Even if you do this, one person will technically have to flee (you don't have to do a dice roll if it's a compromise). The one who is fleeing will return to Quest Mode First.