The water pump should be triggered by low pressure. When you disconnect from city water the internal water lines will still be at the pressure from the city water line pressure. You can verify this by turning off the water pump and disconnecting from city water and turning on a faucet - water will flow for a bit until the pressure is relieved. In fact even with my water pump if turn it on until it pressurizes the system there is enough pressure in the line for a few toilet flushes at night without turning on the pump.
