What kind of cloth does the OP have, and how new is it? I always thought this was from certain cloths made with stain resistant chemicals until the cloth breaks in.
I cleaned my balls about 2 weeks ago to a beautiful shine without any spots.
My Simonis 760 is about 5 years old so it s way more than broken in.
My balls got these marks on them within a few minutes of starting play. But over a couple of days they became worse. I think that this is a cross product of slightly dirty cloth and the contact pressure the balls go through when they collide; the grease on your hands when pulling them from pockets does nothing to help.
I can tell you that soaking the balls in water for 10 minutes makes getting the spots off a LOT easier.
Oh By the Way:: I use a rag that was once used to apply car polish to a car of mine, and then I use this cloth with the polishing particles still embedded to bring the luster up on the surface without adding the sealant of the original car polish. Been using this rage for 5-odd years. It polishes the balls up good, and is also good for removing chalk marks on the cue ball.