The system is under constant tension between the racks and return springs. When the chronograph is stopped, the brakes for each advance pawl (shown in purple on both diagrams) move into place so that even though the system isn’t pushing the rack continuously forward, the return spring system doesn’t automatically reset all counters. However, when the lower pusher is activated, it pushes down a spring-loaded block (in red), allowing the carrier reset system (in blue above, which underlies all this and is attached to all three brakes and levers) to shift counter-clockwise. This lifts (and therefore releases) the light blue advance pawl and the purple brakes, regardless of whether the chronograph is running, resetting the system. That enables the flyback function, which restarts the chronograph and resumes counting when the pusher is released (and the spring of the blocker moves back to neutral, pushing the carrier lever out).
Obviously, the gear train (pushed by the mainspring) needs to transmit more force than the return springs are resisting, but not so much that it affects function. It’s a delicate balance of tension. The return springs also act as shock absorbers for the chronograph and counter jump, so that there’s no stutter when the system advances. In practice, the watch worked flawlessly as I activated, reset, and used the flyback function dozens of times while watching the movement to understand it and confirm that there truly was no stutter.