DO NOT under any circumstances use PVA as a tile primer.
Tile adhesive is water resistant, but not water proof. The water will find it’s way to the PVA, once this happens it will become liquid again and come away.
To do it properly, I need more info to advise you properly.
Where are the tiles going, bath or shower area?
Is the remaining skim very solid, it needs to be really. If not, pull it all off using a scraper or equivalent.
What size and thickness of tiles are you fixing? Are they ceramic or porcalain/stone?
Finally, what pattern are you doing? If brick type pattern, the wall really needs to be super flat, unless you’re a pro, even then it’s extremely hard to get it perfect if not totally flat.
Usually you an get away with filling the patches with tile adhesive, not the tubbed ready mix stuff though. Proper cement powdered stuff. Rapid or normal set. Get decent stuff like weber or mapei, bal is way over priced for what it is and no better than weber.