I was watching Born to Run tonight and picked up on some actual evidence to support the theory that John Henry did not jump to the future: After Cameron and John Henry exchange their little "hello" greetings and he asks her if she'll join them, Cameron whips out her knife and closes the door. The door fills the screen and you don't get a visual of the full closure, but you do get the sound of it latching. So we know it's closed all the way. When John and the others arrive, however, the door to John Henry's room is open. It's not wide open, but it's open enough to show that Cameron's closing of it was not that last time that door was touched.
We've got motive: save Savannah, confront brother AI. We've got no pile of clothes on the floor or any other disruption to the room that might indicate a time jump. And we've got an open door. This juror has finally reached a verdict: John Henry is definitely still in 2009.