Ha what are the chances we have just back from fixing a very similar problem, cleaner had used an acidic cleaner and caused a white oxidising on black slate floor, we used a neutral detergent and floor spinner on TM to clean the floor, this did nothing for the staining but left us a good base to work from, we then applied a mix of 50 / 50 true turpentine and boiled linseed oil waited for a while then applied again waited a while and buffed the surface with a cotton carpet pad to remove excess, not a shiny finish but a very natural and almost wet look, if the white marks disappear when wet this could help