Can a card copying a double-sided planeswalker transform?
You are correct about the outcome, but it is a different set of rules that deals with what happens here.

In the case of a Jace token, it can’t transform because tokens cannot exist outside of the battlefield, and can’t ever come back to the battlefield after leaving. With a non-token copy, we have this rule:


  711.8a If a player is instructed to put a card that isn’t a double-faced card onto the battlefield transformed, that card stays in its current zone.


So the Duplicate will remain in exile.