As shown in
this diagram and in the diagram Dave referenced, there is a one-way check valve at the output side of the pump. This prevents the city water source from trying to force water backward through the pump. A good idea. But ...
If city water is connected, the pressure closes the check valve. If you start the pump, then the pump is pumping against the closed valve. In other words, the water can't move. If this were an impeller pump, the impeller would simply spin in the pool of water in the pumping chamber, and no harm would be done. But this is a positive displacment pump. The motor goes around, and the wobble plate pushes against the rubber diaphragm, and the diaphragm has to move. But it can't move, because there is a solid column of water beyond it, and that water can't move. And water is incompressible. So the diaphragm has to move, but it can't move. Something has got to give. Either the motor stalls, since it can't push the diaphragm. Or the diaphragm rips. This is one disadvantage of a positive-displacement pump.
All of that assumes that the city water pressure is high enough to keep the valve closed. If city water pressure is lower, the pump may be able to force the valve open when the diaphragm is pushed. In that case, the pump will actually move water, and nothing will be hurt.
Did that make any sense?
Bill