Why does the pump on a pumped accumulator run for so long after a tap or shower has turned off?

The pump on an AccuBoost accumulator is designed to boost the mains water flow up to 12L/min and to pressurise the system including the vessel within the vessel.

When a tap or shower is opened water is drained from the accumulator and the system, the pump will then turn on to fill and pressurise both the vessel and the system, including any pipework. The pump will continue to run after the outlet has been turned off. How long it continues to run for depends on several factors including how much water has been used and the size of the system.