It depends on what percentages they were working with in the video. If they were doing their strength speed mini-cycle then it may look slower. The speed strength cycle is faster, then the deloading / explosive cycle is as fast as you'd expect.
What is important on each lift is the effort that is put into accelerating the weight. Don't just do the rep. Consciously drive it as hard as you can.
You are training your muscles to build up energy on the eccentric to be used for the concentric portion. This is the building of the stretch reflex. This is why bands are very important with dynamic box squats.
Most people just getting started can not sit back because of hamstring weaknesses. If your hamstrings are sore, it may be that they weren't hit before, and that you need to bring up their work capacity. It doesn't hurt to have hamstrings and abs that are too strong.