If the thermal readouts of the hygrometers have previously been accurate, I would trust them over the wineador's built-in gauge. That's because the works of the wineador are having to work harder than usual during start-up and the wineador's built-in temperature sensor may be located near the cooler itself, while the rest of the interior hasn't cooled down yet; the hygros are (I'd presume) on shelves along with the cigars, which should provide them with a little insulation against conductive cooling.

As for the drop in humidity, I'm going to make two assumptions. One, the HF beads are in the bottom of the wineador, which is probably the coldest part of the unit. Two, the hygrometers are higher in the wineador, probably on Spanish cedar shelves along with cigars. If these assumptions are valid, here's what's happening:

As the wineador cools, the interior walls (at least near the bottom) cool first and then take heat from the warmer air. Cooler air is denser than warm air, so it tends to stay near the bottom; but cool air doesn't hold as much absolute humidity as warmer air, which helps explain why really hot-and-humid summer days are so oppressive while cool-and-humid days in early spring and late fall are much more comfortable. (The only times when absolute humidity and relative humidity are the same are at zero percent and 100 percent. Between those two extremes, meteorologists and cigar lovers need only pay attention only to the RH.) The important thing is, when the moisture in the colder air condenses and/or returns to the beads, the drier air is then lighter and can rise. (Rainclouds do the same thing to get over mountains.) This dry air is what the hygrometers are measuring; yes, the air around the hygrometers -- and cigars -- really is too dry.

If the RH stayed that low very long your cigars might dry out enough to suffer damage; more likely, an RH in the mid-50s to mid-60s would only slow the aging process, and make them too dry for proper smoking. The good news is that HF beads regulate relative humidity rather than absolute humidity. When the temperature equalizes throughout the wineador, the beads will be able to respond to the lower RH by releasing moisture.

You might be able to speed the process slightly by misting the beads with distilled water, if they are not already close to being fully hydrated. But odds are, you don't need to do that; the RH should return to where you want it to be before the cigars' fillers know anything has happened, and the binders and wrappers will return to your desired RH quickly, none the worse for their brief experience.

If you have any doubts, or if the RH hasn't begun rising by morning, transfer the cigars to ziplock baggies or tupperdors with Boveda packs until the temperature and RH within the wineador return to where they should be.