Here's a link to a video. At about 1:03, you can see that the inertial sleeve actually appears to move forward during the initial phase of recoil. That is because it stayed still (inertia) while the gun accelerated backwards.
https://www.youtube.com/watch?v=XgMaOdkQCkU
Furthermore, as the recoil continues, you can see that the bolt/inertial sleeve, after the inertia spring is compressed and decompresses, are moving backwards faster than the gun is due to the inertia spring's force.
Here's a closeup showing that at the initial moment of recoil, the inertial sleeve stays still (appears to move forward relative to the rest of the recoiling firearm). This demonstrates that the gun is not momentum operated. The sleeve doesn't recoil with the gun, it stays still initially while the gun recoils. It doesn't move backwards until after the inertia spring decompresses and drives it backwards.
https://www.youtube.com/watch?v=TvgtB2hTWaI
Here's a video from Benelli explaining how the system works.
https://www.youtube.com/watch?v=hLro9wdHq44
The explanation is completely consistent with the description I provided above.