I recently started looking at this mechanism again and it really is quite interesting.
This is the manufacturer's animation:
I made my own simplified animation of how I understand it works:
A two-part piston held by a sear seals the breech.
When the sear is tripped by the trigger, the piston can move back allowing air to flow out.
If that was the end of it then the entire chamber would be dumped.
However the is a second valve that separates the de factor firing chamber from the main reservoir.
This is normally held open by a spring but the air flow forces it closed, choking the flow.
This allows the pressure to drop in the firing chamber, and the piston can re-close and be caught by the sear.
The firing chamber then pressurizes again and as the firing chamber and reservoir equalize, the flow choking valve opens again.
The cycle can then be repeated.
Another clever thing is that the drop in pressure is linked to a piston that indexes the rotating magazine.
It really is something I had been playing with
more than a decade ago:
That didn't work very well, the stroke of genius is the addition of the choking valve to enable the piston to cycle.