They will not dye the leather, only raw leather can be dyed. It will be a top coat much like paint, proper prep cannot be stressed enough. If you go to an upholstery shop they will probably use a product line called SEM, I've used it before and it works well but I would suggest looking up a product called Leatherique, nothing better. You can easily do this yourself if you're the least bit handy and can follow instructions well. Just like painting a car, prep is everything and will determine the results. Complete color changes are worst because of show through from scratches and wear over time, Leatherique has a top coat that helps with this, plus if you do it yourself you can touch it up yourself.
BTW if an upholstery shop will do a proper job for $100, go for it, but I'm sceptical. It's time consuming to do this properly. I'd be asking what they use and how they prep it.
The steering wheels were done with Leatherique, painted on with a brush. You can spray it too for larger stuff if you want.