Is it normal for the voltage tester to beep when touching the refrigerator frames?
Since it's only detecting it near the water dispenser, everything is most likely working properly.

The water dispenser will likely have some electrical wiring near it to run motors or valves or what have you, and that is what it is picking up.  They are probably run quite close to the surface of the frame.  Your meter is designed to detect up to about 2 inches away from the wires.  That distance might be different through metal.

Other appliances you tested probably have their wiring further inside the unit, or shielded better.  If you tried hard enough, you'd probably see similar behaviour with other appliances near where their motors are.