A pump controlled by switched taps should run when ever any of the taps are opened, the fact its happening on both cold and hot taps points to fault with the pump it's self, but some caravans were fitted with a pump control circuit:-
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These were designed to try and stop hot/cold surges and some versions also tried to prevent the pump from running when the cold water tank was empty.
If you have one of these fitted it might be playing up. Otherwise it points to a faulty pump.