Most likely the mason is correct. Fixing can be a bit tricky. What types of primers/sealers are available in your area? These spots/areas need to be sealed to stop the oily stuff from coming through the finish. Applying a shellac or shellac primer is the best way to seal them up. But a stain resistant oil based or acrylic primer will also work, this could take 2 coats as the first coat will lift some of the oil into the primer.
You should also consider sealing the outside from water seepage if this is a possibility.