Looks like cheap stuff and probably not really any good for digital printing, even without the lifting.
Turn your heat settings down a bit on your printer, and try it.
easiest way to start, would be to diagnose whether its simply the media. you might get a few more credible troubleshoots if we knew the material and the printer at the start of the thread.
unknown avery vinyl could be the culprit, as that brand still carries a LOT of question marks for me. could also be something silly like adhesive/stickiness on your pinch rollers lifting vinyl off the liner as its traveling through the printer. ....and i rant.
MPI3320 seems to be listed as acceptable for all types of printers... gotta just be the old/cold calendared vinyl going thru hot printer.
Forgot to mention Mutoh1624