that would be a  great clue..   'when does it kick back'.

During starting?... or  the final  revolution  when shutting down/failed  attempt  when starting.

Seems like  every small motor that's  kicked back for me over the years,  is one that's been working the snot out of, and   shut down  while  quite hot..  and on that last  revolution,  the  gas  fires  against the  piston.. (no more  inertia in the flywheel to  carry it through)  and  bam.   backwards it goes.. the starter pawl   'catches it'.
I'd  try  letting it  cool  10-15 seconds  no load,  idling.     At least   shut it down after  bringing it back to idle.   

Or,  put a  chunk of  light compression spring on the rope  about  6-8 inches long  to keep the  pull handle  off the  'stop'