Up and down, or a discontinue, is the correct violation. It's not technically a travel since he had his dribble, but you cannot jump with the ball and come back down with it. Doesn't matter if he had his dribble or not, that's a turnover.
I replayed it once and wondered about that call. Let's see if I got this right:
He had not yet given up his dribble.
He left the floor with both feet and both hands on the ball.
Instead of shooting it, he put it back on the floor...now here's where it gets tricky....
...after one of his feet hit the floor and gathered the ball back again.
That being the case it's a clear travel call.
...let's say before he came back down, which I'm not sure was the case.
That too would appear to be a travel call as well since that is the same as moving your pivot foot before you begin to dribble.
This should not be confused with what takes place after one is in the act of dribbling. In that case the player can take either two steps and up or the jump-step (1 step and a 2 foot plant), but in either case the player has to continue the play with a shot or a pass. I believe if a player does a jump-step and holds the ball, they'll get called for a travel, but I might be wrong on that one.
Quite loosely related to this topic, If a player throws it off the backboard to himself where he takes a whole bunch of steps in between, wouldn't that be a travel? I'm not sure they call it that way, do they? I can understand if it hits the rim, that would be considered a shot and a player can restart with whatever they want to do, dribble, pass or shoot it again.
How about when a player loses control of the ball where he catches up with it and continues with his dribble w/out anyone touching it in between, I'm not sure if they call that one consistently one way or the other.
One last observation - I see players change their pivot foot quite often without getting a travel call. It often happens either when they first catch the ball or terminate their dribble. It's very hard for an official to catch which of the two feet is the established pivot during that instance when both feet come to a stop around the same time. I don't really have a problem with it since it is really hard for a ref to catch, but if you go by the letter of the law it is a travel when the player starts with one foot as their plant foot and then switches to the other as the pivot. This is most noticeable in the NBA where the players are real sloppy when it comes to establishing the pivot. The rule of thumb is if the foot work looks sloppy, i.e. happy feet, it's probably a travel, but IMO as long as there's not real advantage gained, no big deal, though sometimes it makes the game look sloppy. For some reason Paul Pierce is one who comes to mind that seems to have a lot of tap dancing before he goes on with his move.