If you have a bladder-type pressure tank, you should drain it of water and verify that the air pressure is correct. It might have lost air over time or have a bursted bladder. There is a post explaining more about that here- http://www.terrylove.com/forums/show...nk-Maintenance
A hose spigot can flow a lot of water relatively quickly. How fast your tank fills is relative to the rating of the pump and motor. In a perfectly sized system, when water is flowing from a large spigot such as an open hose or bathtub, the pump will run continuously without cycling on and off. Cycling the pump is hard on the motor, and it is better that it runs non-stop. IF the pressure falls below the cut in pressure of the pump, then your are using more water can it can pump. As long as the pump can maintain or increase the pressure while water is running, I wouldn't consider it a problem.