Sturgeon are known to be jumpers. Generally speaking, Sturgeon (no matter the species) need relatively cold water with high levels of dissolved oxygen. The dissolved oxygen and cold water go hand in hand. It's difficult to keep dissolved ox high without cold water. Furthermore, Sterlet and other Sturgeon species can be quite active. The popping of the nose out of the water and jumping could be due to the pond being too small.
I would think that water for sterlet should be no shallower than 5' deep at 75% area of the pond.
Sounds like they are either hungry or extremely bored.. I wouldnt buy any from there, getting starved sturgeon back to normal weight is near impossible.