I have the same thing hapen using that Lyman media, I guess the red stuff if something like Jeweler's Rouge. I've never actually bothered to clean it off as it doesn't seem to cling on and Lyman don't seem to advise trying to get rid of the dust either.
If you are tumbling them with case lube on them, i.e after re-sizing this can really attract the stuff and it's not good. The spray on Hornady One Shot claims that it will be taken off in the tumbler as it soaks into the media...it does to a point.
If you are really concerned about it switch to the non-treated Tuff-Nut media which does an equally good job.
I have also found that the best way to remove any resizing lubricant along with any burn rings is to wash the cases in Birchwood Casey Brass Cartridge Cleaner.