There are several reasons a roll will tear on rewind.  On the players
produced by Aeolian in the 1960's till they quit production around 1980
the most probable cause is that the take up spool flanges are too far
apart.  As the roll is played and the tracker shifts left to right or
right to left the paper would telescope on the take up spool left and
right.  As the roll rewinds it tears up.  I used to put the take up
spools on a table saw and cut them down so the paper could not
telescope too far.

My two cents worth.
Don Teach