Dial refinishers are for the most part very hit and miss - even the "good" ones can be. In the circle of watchmakers I am ion contact with there are almost constant questions about who is the best and you will almost always hear good and bad feedback about any one particular vendor. Often these vendors will specialize in a particular brand. I sent a vintage Rolex dial to a very well regarded company in the US who was the "top" refinisher, and they literally destroyed the dial. They made a new dial from scratch, but it was a disaster and pretty much useless.
For whatever reason dial refinishers tend to be highly variable in their timing, quality, and ability/willingness to rectify a problem. Someone who is highly regarded for a while can quickly fall off the top of the heap and be a problem vendor in a very short time - it's quite puzzling.
As noted you really have to work closely with whoever you are using and make sure they know what you want. Keep in mind these guys work with a broad range of customers, from the guys who are flipping the "ooh shiny!" examples on eBay and don't care about details, to people who want accuracy like the collectors do.
Unless you specify otherwise (and also want to pay for it) most refinishing companies will get your dial in, look at their inventory of dies, an select whatever is closest to what you want and use that. If you want an exact match, most likely they will have to make new plates, and those are not cheap. If you are into multiple colours or finishes on a dial, the cost can quickly escalate. The company I use charges $90 per plate...
Even if they get the general layout correct, often the font will be slightly off, or the printing will be too thick - these details seem to escape most refinishers for some reason.
Good luck with your project!
Cheers, Al