Correct me if I`m wrong peoples,
I don't think that it's a deluxe. The deluxe jazz's have four control knobs on the control plate, which doesn't leave room for the jack to go through the control plate. The non-deluxe Jazz basses only have the three knobs on the control plate, which leaves room for the jack to be plugged in there.
I'm going to assume that it's just an American Standard or Highway 1.
/edit:

Here is an image of him with one of the jazz basses. The bass in video looks like it has an olympic white finish, and a tortoiseshell pickguard. He normally plays a Marcus Miller jazz bass (which has the distinct pickguard).