What is the mechanism of action of PVA glue?
The glue isn't curing

Because it has no exposure to air.  

Effectively, you haven't applied it, just put it in a different bottle.  

The moisture of the stuff is softening the pine wood around it. 

You're lucky, too. If it had cured, you would not have gotten that screw out in a million years.  You're really playing with fire on this one. 

Leave the screw out for a week, see if that helps.   

And if you want to do that in the future, either a) drill it out and glue in a dowel of similar softwood, b) mix a thick slurry out of sawdust and glue, or c) if you suspect wood deterioration, hit it with an epoxy product called Git-Rot, which will soak into the wood.  But in all cases you wait for glue cure before putting any screws back in.  And if you want the glue to cure at a definite, positive rate, use epoxy glues.