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Deadband is also known as hysteresis and is the amount of a measured variable (pressure, temperature, etc.) between the point where a switch closes and then re-opens. It can be implemented is software if you have an analog input (i.e., open at 1.02 PSI, close at 0.98 PSI) or designed into a switching mechanism. Often the deadband of a switch is fixed and cannot be adjusted. A typical example is in a wall thermostat in your house.
Power supply wires connected to wrong screws in pressure switch. Power supply wires need to be connected to the two connection screws that do not already have the motor wires connected to them. If the power wires are on the same screws as the motor wires, the switch cannot shut off power to the pump.