why is my water pump keep going on and off only when i use it?

The aerators on the inside faucets restrict the flow enough that with only one open the pump can reach cut off pressure. When you use the hose bib or more than one faucet the pump doesn't get to cut off pressure so it won't go off and on. Your brand new tank needs the bladder/diaphragm precharged. The air cushion it provides will stop the rapid cycling of the pump. There will be a tag on the tank stating what the precharge pressure should be. The tank will need to have all of the water pressure bled off and a faucet left open when you precharge the bladder

Your pressure tank is water logged. You should have a large bubble of air inside the pressure tank to provide equal and constant pressure on the water. It also saves your pump from burning out caused by constantly coming on and off.

Check the pressure tank, somewhere on the side of it should be a valve like a car tire has. Use a portable air compressor and put 35 lbs of pressure in the pressure tank.

The air inside the pressure tank will slowly be absorbed by the water going through the tank and you will have to pressurize the tank again when that happens.

Maybe your bladder tank lost its charge on the bladder.