When a pump runs when there is no known water use, there is an unknown water use; commonly called a leak.
It can not be caused by a pressure tank and it can only be the switch IF the points are stuck closed AND, the pressure is higher than what is supposed to cause the points to open and shut off power to the pump. Does that make sense?
So there is a leak, shut off the water past the pressure tank, watch the pressure gauge for 5-10 minutes and see if the pressure falls, if it does the leak is between the tank and the foot valve or check valve in the well' jet pumps have a foot valve , submersibles have a check vlave in or on their outlet. If there is a check valve at the pressure tank, the above will not work because that check valve hides a leak between it and the check or foot valve. That's why there should be only one, and it should be in the well.
Do not hire plumbers that are not willing or capable of pulling drop pipe and/on submersible pumps, and only few are. A pump guy or well driller is best. And never replace anything without proof that it is bad and the cause of the problem.
Your power cable may be undersized for the size of the new pump or, shorting out or, there may be something wrong with the shrink warp he used to connect it to the motor pigtails (they must be water proof) and something is shorting out. Or a bad motor.
You need someone to do the proper ohms, conductivity and amp tests before you do anything.
Get a multimeter and amp gauge and roam around here:
http://www.franklin-electric.com/business/WaterSystems/service/AIM/page-45.aspx