Hi and welcome to the forum.
First and foremost if the taps are still dripping when they are turned off, then the tap seals have failed. Depending on the model of the taps you may be able to get new seals, but more likely you may want to replace them.
If the pump continues to run when the taps are off, then you have a faulty microswitch in one or more taps. Again its sometimes easier to change the taps than try and find and fit microswitches.
If the taps drip despite the pump actually turning off then I ll bet you have a water heater. The heater has a a 10L tank and it will always have a small air gap at teh top of the tank ( this is necessary to allow the water room to expand as it heats up. When the pump runs, it pressurises the pipework to deliver the water but it also will pressurise the heater tank. When the pump stops the cold water pressure will drop away very quickly, but the pressurized air cap in the hot tank will continue to deliver water to the taps until the pressure is lost. This could be the trickle you get at the leaky taps.