Tony Irwin wrote:
Many flies pick up mites (Acarina) when they emerge from the puparium. Many mite species (and also pseudoscorpions) rely on attaching themselves to flies and other insects for dispersal. When they have flown some distance, they leave their host and start life in their new home. Most of them do not feed on the host, just use it for transport.
Many of the photos on this site show flies with bright red water-mite larvae attached, but the mites can also be pink, yellow or white.
If you can get a photograph of what you saw, we should be able to tell you what they were.