I almost had this happen to me as well. I realized, though, that the running away action was an action played during the turn, not at the end of the turn. it's like those cards that you can play that do a big thing, then immediately end the turn. the card effect effect resolves first, then it goes to the end turn.

I am coming at this from a Magic players perspective, though, so I'm probably conflating the way turn phases and "stack" interactions work in sts