How the dampener works to reduce pulsation?

Technically, it is an analog of a resistance-capacitance filter. Which is a device that restricts the passage of higher frequency components.

In a mechanical system such as the 'shock absorber' in a car, the resistance part is provided by the fluid passing through a small hole; and the capacitance component by the volume of the reservoir.

A shock absorber in a car really damps out vibrations, it has a smaller effect on real shocks.