Bonding primer problems
Most acrylic ( waterborne) primers will only stop some stains.
Bin is the fail safe.
If you are only seeing some spotting, not overall, just spot with BIN , then respot with your stix just to test if you got it. Both dry pretty quick so should give you your answer quick. Just watch the build up of brush strokes so that doesn't show through to your finish.
BTW- why 2 coats of primer? One coat ( besides the bleeding issue) would give you the bonding needed. Then Paint ( or above in this case) .
2 coats of primer does not make the bond better.
"It's better to come here with questions before you screw up than to come here after and ask how to fix them."- JS