This may be happening because there is a check valve in the water line between the tee and the house. When you turn on a faucet in the house and the pressure drops, the pressure switch turns on the pump. Between the well and the check valve is where he tied in to your water line. When you run the field faucet, the water line may have a little pressure and then it stops. If there is a leaky foot valve or something and then you may have no pressure. The only way to start the pump is to run the house water till the pressure switch turns the pump on again. You could relocate the check valve so it is at the well or it could be in the line anywhere before it tees off. The pressure switch would sense the pressure drop anywhere in the line back to the check valve.