Yes, I'm unsure whether he's just guiding both bodies of if he actually pushes them, but if, it's just slightly. The vast majority of the additional momentum of the hammer comes from the ball. You can see just how low the ball bounces back. Not even half of its initial height. The 'missing' momentum (or energy) is mostly transfered to the hammer, the rest is dissipation.

The ball gave a big chunk of its energy to the hammer. The ball doesn't have the density that the hammer does (we think of the hammer as much heavier as the ball, but in reality that big yoga ball might be around around 2/3 the weight of the hammer), but it's the overall weight that matters.

So if 40% of the weight/momentum of the whole system is in the ball going down, and half of that gets transferred back to the hammer coming up, while the hammer has 90% of its momentum (originally 60% of the system) preserved in the bounce, we're talking about enough roughly 74% of the original momentum (54% of the original system momentum plus 20% of the original system momentum) pushing 60% of the original system mass, enough to exceed the original height.

Some of the height is lost to the angular momentum of the spinning hammer, but one can see how this experiment could've bounced the hammer higher than it started, even without any downward momentum being contributed by the guy pushing it downward.

From the spin on the hammer after it hits his face it looks like there was a lot more energy left, but I'm no physicist so I have no idea where it's from.