My interpretation based on the animations is this, I could be wrong so please correct me if this the case:
- At rest, the poppet is held forward due the gas pressure behind it. The gas that's holding poppet forward will be used to make the bolt move later in the firing sequence. Also at this point the bolt is held back via a spring in front of it (first animation).
- As the poppet uses a larger area rear section and a smaller area front section, the gas pushing against the rear of the poppet has more force than the gas in front of that rear section, that's why the poppet is held forward sealing the gas chamber which holds the poppet assembly.
- The gas behind the larger/back end of the poppet is purged/vented by the solenoid to allow the poppet to move back via the pressure in front of it. The gas from the rear of the poppet is routed via the solenoid to behind the bolt.
- The burst of gas routed via two ports from the solenoid (coming from the rear of the poppet, remember?) forces against the rear of the bolt, propelling it forward collecting a paintball along the way.
- There are 2 inline ports for the gas to push the bolt forward, this is to give it a slower (softer) start to the movement of the bolt, and speeds the bolt up once it clears the second port.
- The rearward movement of the poppet allows the gas in front of it to be released to fire the ball.
- When the solenoid resets the gas is allowed build up behind the poppet again and force it forward to seal th poppet.
- The spring at the front of the bolt resets it to it's rearward position.
Phew! i hope i got it right