As you mentioned, Unsubstantiate says to return it to its "owner's" hand. You would be its owner even if they are casting it.
Something to keep in mind: a card that you don't own can never go to your hand, library, or graveyard. That card will always go to its owner's referenced zone.
Hi! My friend and I are pretty new, but we were hoping to settle a dispute. He used Gonti, Lord of Luxury to exile and then cast my Jace, Bryn's Prodigy. When I use Unsubstantiate afterward, the card demands that Jace be returned to its "owner's" hand. So would he go to my hand since I own the card, or his hand since he paid mana to cast him?
Awesome! Thanks for helping out a total newbie!!