the solvent in that fast cure glazing putty may have been something fast and agressive like hexane or similar fast flash solvent.. and likely disolved the primer.
i have been able to remove 'rattle can' overspray off of cured hardend paint, using a rag, wetted with mineral spirits or naptha, then just the corner dipped into laquer thinner, even after the rattle can paint had been on for hours.
had a buddy over at my shop and he was spray painting some lil widget he had made, and right next to that lil red widgit he was painting was my ford grey tractor hood.. I didn't notice the oversprayed droplets until much later.. came off clean though..
so it all depends on the solvent in that glaze putty, and the fact it was not a catylized / cured paint.. etc.