The problem is that the style name isn’t being imported. After some tinkering (I had to turn off the “include styles information in exported file” option and turn it on again) I now have the formatting for those styles showing up in the word document.
The bug–or so far unimplemented feature–is that the style name isn’t imported to word. Since that is the simplest way to get Vellum to recognize parts of the book, it would be very nice if it were.
My wild guess is that it’s something like a similar problem I had a while back with e-pub compiles: Scrivener is just ignoring the “Overide Name” entry.
At this point I think would relabel this a bug–If I knew how to do that…