This could be from the screws or it could be extractive bleeding from the paneling. Apply a shellac primer to the spots and touch up the paint. This should seal any bleeding.
With a good stain blocking primer the type of paint doesn't matter. Oil based primers like Kilz or Zinsser Cover Stain do a good job, stopping most stains. Galvanized screws would have been better but aren't necessary with a good oil based primer.