Normal........
Water pump pressure switch is reacting to line pressure.
When using a faucet the line pressure drops and pump comes on (on demand system)
Pump discharge pressure builds up until pressure switch opens which turns pump off but then line pressure drops and pressure switch closes turning pump back on.
This on/off hunting is normal when demand is lower than supply
Pump can supply more water than faucet can run --------turn on both hot/cold wide open or open another faucet and pump will run continuously (demand higher than supply)
A inexpensive cure........add a 2 gallon accumulator tank on pump discharge line.