Increased mite fall occurs within a day of adding iron to the bees' diet. This effect lasts for 1 or 2 days.
The mite fall can be comparable to the fall of ticks. Both ticks and mites are octopods. In research into the tick conducted at the Amsterdam Medical Center (AMC) in Amsterdam, the process by which the tick infects its host is described in detail. This provides a good understanding of the infection process by the tick. This is also applicable to the infection process of the Varroa mite in bees.
The Borrelia bacteria, which causes Lyme disease in humans following a tick bite, plays an extremely important role in the infection process. The tick carries these bacteria in the intestine. The tick falls off the host as soon as it has absorbed sufficient blood. The infection with the Borrelia bacteria may have already occurred. It has been established that this usually takes place after about 24 hours. In other words, a certain passage of time is necessary to transfer the bacteria from the tick to the host successfully.
As soon as the tick bites the host, it takes up some blood. This blood reaches the tick's intestine and causes the bacteria to be released from the gut wall. The bacteria then move to the site of infection. There, it inhibits blood clotting and also suppresses the immune response in the host. The tick can then continue absorbing blood easily. See http://www.amc.nl/web/Het-AMC/Nieuws/Nieuwsoverzicht/Nieuws/Schatgraven-in-speeksel.htm (in Dutch) for a description of how the tick infects its host. See http://dare.uva.nl/document/338192 (In English) for a thesis about the tick, the Dutch summary can be found at http://dare.uva.nl/document/338205
The role of iron
It is plausible that the iron in the blood plays a decisive role. After all, it is known that this affects bacterial biofilms. In other words, the bacteria present (Borrelia) are released by the addition of iron. The bacteria are no longer hidden in the biofilm on the intestinal wall where they are safe and immeasurable.
If the bacteria are released too soon, for example by administering extra iron, then the bacteria are exposed to competition from other intestinal bacteria. Consequently, there are too few Borrelia bacteria to successfully infect the host.