the fabric shouldn't slide in the tracks on the roller, the plastic is supposed to be left long enough to run all the way out the ends of the roller tube and then be curled back into the roller tube before the torsion spring assembly is put on. i'd get it centered and put some very small screws, maybe even pre drill and use wood screws instead of machine screws so there's no head to wear through the fabric.
installing my new awning last month, it didn't take long to realize if the fabric isn't centered on the tube AND inbetween the arms in the track at the top of the wall, it's not gonna roll up straight. that's why the legs don't 'fasten' together correctly or why it doesn't roll up straight.
and yes, you should use screw one screw through the awning fabric where the plastic rod that's sewed into the fabric slides in the track, one about an inch or inch and a half from each edge holds it nicely in place