Hello George,
I have come across this in caravans where the water pump is controlled by a pressure switch.
The water heater has a none return valve fitted to it cold water inlet. If this has stopped working properly, as the heater has a small air cap (which is essential for it to work) when you open a cold tap, the pressurised air cap pushes some of the heated water back through the cold water inlet and into the cold water pipes. this continues until the air cap has fully expanded and the pressure drops enough to turn the pump on.
The other way that this can happen, is if you have a separate mixer valve and water control valve on the shower. The mixer valve if left at an intermediate temperature setting effectively joins the hot and cold pieceworks together. So as above the air cap in the heater pushes hot water into the cold water system until the air cap is fully expanded.
Solutions, in the first case have the heater none return valve checked, and if it is the mixer valve then both hot and cold lines should have a NRV fitted to prevent back flows. Or make sure the mixer valve is always left at an extreme hot or cold.