Joint possession goes to the offensive player, but I don't think that was joint. I think Jennings had it, not Tate.
Just to play Devil's Advocate (because I think that was a pick),
when is the joint possession determined? That is, is the play judged by when the players land on the ground with their feet, when they touch their knee(s) to the ground, or when they come to a complete stop? Is this impacted by the going to the ground rule? I've no reason to believe it does, but it may impact who is deemed to have possession.