I'm running a vs-540i and use the Avery 1005 SC material all the time. Never had any problems with it sticking to the back of the liner. Lots of trouble though, if you let the printed face touch itself.
My first thoughts are:
1) It could be the non-OEM inks. Never had personal experience with them, though.
2) It could a super-high level of ink saturation, so the ink doesn't dry enough before touching the liner.
If you have some kraft paper or left over liner from other prints, you could do another test. Print a section of your artwork (not the entire run) and roll it up with the kraft paper or the liner. Does it still stick?