It's a matter of degree. As the pressure tank discharges, the water pressure will go down. When the pressure goes below a certain threshold, a pressure switch will turn on the pump, and the tank will start filling and raising the pressure. When the pressure goes above a different threshold, the switch will turn off the pump and the pressure should be maintained as long as no water is used. When water is used the pressure should fall slowly. The difference between the two thresholds is called the hysteresis; too little and the pump will be turning on too often and running too briefly, and too much and the pressure vary too much.
If the pressure fluctuates "too much" (where the speaker gets to define "too much") then it might be a problem with the pressure tank, the pump pressure thresholds, or (escape clause!) something else. But that all depends on what the system is designed for. In a recreational vehicle, the water pump generally turns on as soon as you turn on a faucet, which is fine. In a house, though, this would be a problem, and cause pump wear and tear as well as annoying fluctuations.
I'd talk to the inspector and get details about the problem he saw and what he thinks the solution might be. You might also talk to a plumber with expertise in well systems.