Here's one of my four meteorite dial watches. It's a customized Lüm-Tec M23 with a gibeon dial.
I collect rocks, fossils, meteorites, etc. Ten years ago I was at the big Tucson Gem & Mineral Show, and a dealer had a stack of gibeon dials. Basically they cut a cylinder out of the meteorite, drilled a hole down the middle, sliced it like a salami and then etched the slices. IIRC, they were 36mm, as that's a standard Rolex dial size. I emailed Lüm-Tec and they said that the dial should fit their M-series. So I bought two, in case they screwed one up. They didn't screw it up, so I had them put the other dial in a V-series watch (I'll find/take a pic of that if anyone is interested).
As was previously mentioned, nickel-iron meteorites tend to rust like crazy. They're around 90% iron. Before the acid bath, it just looks like plain, shiny silvery metal. The cross-hatching is called Widmanstatten patterns. These are caused by the lump of molten metal cooling over hundreds of millions of years in zero gravity, which has two different nickel-iron alloys crystalizing. Gibeon is VERY stable. I have some slices and spheres that took over a decade to start showing signs of rust, living in a high humidity part of the country, and even then it wasn't much. My muonionalusta, which is the same as that auction watch, and most meteorite dials today, rusts like crazy. The first piece of that that I ever got started rusting inside of six months, when I was living in fairly arid Los Angeles. They are not particularly radioactive.
I had my rusting meteorites "repaired" and stabilized earlier this year by an expert. It's not a terribly complicated process, although a bit time consuming. For the rust, they soak the meteorite in a chemical bath (acid, I think), which removes the outer layer and the rust, leaving a shiny polished sphere/plate/whatever. They they soak it in acid to bring out the Widmanstatten patterns. Then they soak it for a few days (maybe a week or more) in another chemical bath to extract the chlorides from the meteorite, which is what attracts the water and causes the rust. The final step was to apply a clear coat so that it won't rust again. I'm not wild about the clear coat, personally, but it beats rust.
Each meteorite has a different Widmanstatten pattern and an expert can tell you which meteorite it is just from that. Gibeon and muonionalusta look almost identical though, and are (IMHO) the most attractive. in the 90s, Gibeon cost about $20/lb or less than five cents a gram. Today it's something like $3-4/gm. Mostly because Namibia made it illegal to export at one point. Muonionalusta (from Sweden) is about half that cost and there isn't any restrictions, so that's why it's very popular. My other two meteorite watches are Zelos. They make some nice and very inexpensive models (like $500-600 for a meteorite dial watch) although they tend to sell out very quickly.
The dials used in commercial watches (as opposed to mine) have been treated in some fashion to inhibit rust. Also, under normal use, very little moisture is going to get into the case to induce rust.