Hi Daniel B,
First, the Windsurfing School is more about the basics than fairly advanced moves like the Slam Jibe.
Also, there seems to be a few different interpretations as to exactly what a "slam jibe" is.
One interpretation is that it's a quick "sink/pivot" jibe. It's also called a snap jibe!
Snap Jibe : A jibe performed by heading upwind and aggressively standing on the tail and whipping the board around using the tail as a pivot point. Sometimes called the Pivot Jibe or Slam Jibe.
If this is what you are trying to do, check out this link.
If you are trying to do some other type of slam jibe, perhaps you can describe it for us.
As far as your question, my guess would be that if your board is kinda "jumping up out of the water" you are "stomping" down with your back foot too hard/too fast.
This drops the tail suddenly and the board wants to shoot up out of the water.
From the little video clip, you can see that Chris P. gets everything set up, then presses down with his back foot pretty hard, but not so suddenly, this sinks the tail so the board can pivot around it. It's more that he brings his weight back onto the back foot and almost "pulls up" with his front foot, so it's more a "weight shift" than a quick pushing down with the back foot.
Hope this helps,