Having had another look at your image, I'm not entirely convinced that PVA is the cause of your problem.
Plasterers use PVA to help the skim coat adhere, so that would be underneath the plaster and wouldn't cause this issue. The cause of the problem would be if the PVA was applied to the surface of the new plaster, before painting.
Presumably the initial mist coat was watered down sufficently, but that can't be controlled now.
I can see what appears to be plaster dust stuck to the back of the flaking paint. Is that the case?
If so, it shouldn't be doing that if PVA was the cause, as the PVA would have entirely sealed the plaster, which is what stops it absorbing your mist coats of paint.
It could be that there was just plaster dust on the surface, which has stopped the paint adhering properly, or even that there was moisture still in the plaster which has caused the flaking, as it dried out. If this is the case, scraping off and wiping away all dust with a damp cloth should be all that is necessary to overcome the problem, before applying a new mist coat.
You will probably need to level out the area with some fine surface filling, after the mist coat, then re-mist that filler and paint as normal. Hopefully, this is all you will need to do!
If PVA is the cause, no universal solution is really out there.
You can try scraping away all of the loose paint and sanding the surface, in an attempt to remove any PVA film, then mist coat the bare plaster and continue, as above. Sometimes it works, sometimes it doesn't.
Another option is to use a high grip primer to see if that adheres to the PVA. There is no guarantee that even this will work, and most manufacturers won't recommend these primers for such an issue, even though some may actually work.
Oil based undercoat can sometimes work wonders in all sorts of situations, so if that's what you meant when you asked about 'none water based paints', then it could also be worth a try.