I say the well is going 'dry'; the water is falling to the inlet of the pump and the the pump sucks air and the pressure falls and the safety cut off type switch shuts off the pump as designed. Start water conservation by spreading out water uses.
I say the air volume/pressure in those tanks should be checked and adjusted to be 1-2 psi less than the cut-in switch setting done by draining the water from the tanks. There should also be 20 psi differential between cut-in and out. Low air volume/pressure will cause shorter cycling of the pump and premature tank failure while wearing out the motor and increasing the electric bill.
IMO the plumber is correct in wanting to use less water by decreasing the pressure settings. I don't agree with two pressure tanks that require more water to be drawn from the well each time the pump runs. And with higher pressure switch settings, that causes the house to use more water (the gpm rises) all while you have a low producing well. It's not the setup I'd use for myself or a customer with a low producing well. And the compressed air in the tank(s) produce the power to move water when the pump is off, so if the volume/pressure is wrong in the tanks, your pressure fluctuation is more noticeable and the average water pressure will be lower than if the system is set up correctly. And when that happens, guys raise the water pressure and make things worse and use more water. Isn't that what has happened?