The only way that type pump would shut off when no water is coming is if it had a "Presscontrol" thing on top of it. Those things have a flow switch that shuts off the pump when there is no flow. I don't see one in your picture, so it doesn't have dry run protection. Also, they use those presscontrol things on low head pumps that can't build enough pressure to work with a normal pressure switch. You need a good jet pump that can build enough pressure, and a low pressure cut off switch to protect the pump from running dry. Those type pumps and the presscontrol things are made to sell and not last very long, which is exactly why the pump companies push them over something like a Cycle Stop Valve that will make pumps last 30+ years.