For me, the sticking of paper fibers comes from leaving it in contect with the CA glue as it starts to cure. Once the thin coat is spread out on the surface there is no need for any more rubbing. For me the need for continuous rubbing came from using too much CA glue and spinning the wood too fast. Once I learned to use a lesser amount of glue (a much lesser amount) and a slower speed, there was no longer any need for continued rubbing because there was no balling up of the wet glue on the surface. .
I had the best luck with the best quality paper towels in the beginning because there was less fiber coming off than with the cheap stuff because I was using the paper towel too long until way after the glue was dry. Now I can use anything including brown paper towels and toilet paper, but still use the best paper towels because they are thicker, work better for me, and they are an interesting argument.
It will take a lot of practice to be able to use the paper towel until after the CA glue has cured. At least it was for me, so I just quit. It is possible to use the paper towel until after the CA has cured if you keep it moving. Stopping even briefly to change directions will give it a chance to stick to the curing glue.
Using too much pressure on the towels has always been a problem, and I had to learn to use a very light pressure while applying the very minimal quantity of glue.
I also chose to do a light sanding with 400 or 600 grit sandpaper between every coat of the CA glue. That made the rubbing of the wet glue with the paper towel not as important, and added very little time to putting on the final finish.