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.
recommend? for what application and what printer? plenty of merchant members here with recommendations if you post the info.
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