water pump behaving strangely

Hi,

I have a problem with a pump used for most of our domestic water.

The pump kicks in immediately when cold water taps are turned on. It takes a little bit longer to start when a hot tap is opened, but there is no delay in water flow.

On turning off the cold taps, when no hot taps are on, the pump goes off.

When a hot tap is turned off however, the pump stays on.
The only way to get it to turn off is to quickly turn on/off a cold tap!

Does it sound more like a pressure problem or a controller one?
Thanks