You need to use your muscles to return the gun to the target after the first shot. This should happen after the first shot is fired and before the second one. So, there's some critical timing that has to happen. That gets tricky when you try to shoot fast splits, like in the doubles drill. As you're learning to do this, sometimes the timing is wrong and you fire after you push the gun down, or you fire before the gun returns. This isn't a flinch. It's part of the learning process. As you develop your grip, stance, and relaxation, the amount of force needed gets smaller, and it starts to feel like "just letting the recoil happen".
Here's a quote from Hwansik: "Most pistols have a high bore axis. Mixing in physics, when we fire the gun, there will be an upward force created by the leverage related to the bore axis and the grip axis. If the operator doesn’t push the gun down, the gun will stop higher than the original spot after a shot."
There's some really good info about this on the PSTG, but it's behind a paywall.
https://www.practicalshootingtrainin...urement-drill/