The best thing you can do right away is go through the cultures and move any newer cultures far away from the older cultures. The next thing is to go through the cultures and get rid of any cultures that are 25 days or older.
IF you have other insect cultures near your fruit flies (example mealworms) move them far away. Next use your youngest producing cultures and start new cultures, ideally dust the flies with a fine powder supplement to help reduce mites adhering to the flies and then place them into the new cultures. Move this to a location far from the old cultures and away from the newer cultures until you can evaluate them for mite oubreak.
The white mites are usually grain mites so they could also be coming from the media or other grain sources near the cultures.. but if you are seeing them in numbers on the outside of the cultures and you aren't keeping other feeder insects nearby, then the outbreak has to be from the fly cultures. To reduce the number on the shelves, you can wipe them down with any alcohol or any disinfectent you use in the house, but if you don't locate the source the mites will continue to go walkabout.
Ed