There's a rough test you can do. Snip off a piece of the backing paper, maybe 3 inches long (Just reshape a tab to go in the slot of the spool and be miserly in winding when loading).
You are going to pull this piece of paper through the rollers as if you are starting a roll. In the middle, put a piece of masking tape. It needs to be a solid masking tape type. Duct tape is too thick, scotch cellophane tape is too thin.
Remove the back. Put the camera on its top. Inside the film chamber you'll see a little black foot on the wind side. As you push this towards the front of the camera, you'll see the lower silver rod lift up. You are going to want to push this foot to its stop. Medium pressure. There will be a sort of a subtle 'oh I think that's it' moment as it engages a part inside but push a little more.
Ok, with foot relaxed, put the backing paper between the spools as if loading. Now push the black foot to its stop. Pull the backing paper through the rollers so that the masking tape passes between the rollers. You will hear it clunk if it is working and the lower roller will release.
If this doesn't pop the Automat, put a piece of film (clip off from a roll) under the tape and see if this does it.
Even if the Rolleiflex doesn't pop with the new paper, you can just wind the film through and then respool it back in a changing bag or darkroom.
The new Kodak paper is one of my test papers all the time because it is thin. Fuji is also thin. Fomapan's black paper is about the thickest I have run across. I test so both work. It usually means adjusting the trip point
