Right, have the print fully encased in the kraft paper so that you cannot see down inside it. Mondo just rolls it in kraft with overhang on both sides and lets it hug the side of the tube to try and keep it from sliding around, which sometimes works, but often you get damaged edges as well.
So, since the print is basically free floating in the tube now, you need to put packing on both ends to prevent the end to end movement.
You only need to be 1/2" smaller in diameter on your roll than the actual tube, basically prevents tube dents from transferring into the print should it take a dent in route.
If it is a high dollar print, I would tube then box to really protect if you have a box big enough, but those 4" yazoo tubes are pretty darn strong.