Using PMS for Sublimation?

Generally PMS is designed on getting an accurate color across all medias (paints, inks, etc), originally designed for getting better matching on paints when a job would be done and you'd go back to do another one, you could refer to what colors to mix to get the precise color you used again. I do not believe sublimation profiles are designed with this matching in mind, unlike say some vinyl printers where their target is oftentimes vehicle wraps and the like where a precise match is more vital.

That being said, Pantone values will always have a "replacement" CMYK/RGB printable value that kinda gets it in the ballpark, so it's not like it's a bad thing to use it, and depending on your art program, it will always get you a consistent print so long as you don't change printers/profiles. It also isn't a bad idea to do logo design with Pantone in mind, as it is still the graphic industry norm for color matching across all fields. Don't expect a 100% accurate result with sublimation. There should be pantone printable charts out there that you can use to print and then sublimate to get you an idea of what the color output will look like. If you're really strict, you can buy a pantone swatch (they're kinda pricey, but great for trying to figure out a precise color out in the field) and see how it compares to your output.

Also keep in mind sublimation itself can vary one item to the next depending on how long you cure and so on, but once you're experienced your result should be similar each time.

PMS is the industry standard, but if they're saying their printer has Pantone spot color matching, unless they're using one of the big boys, they're blowing smoke. A ricoh/small scale epson will instead do the spot color replacement value which as I said, will usually get you in the ballpark. Sometimes especially with blues, you end up more purple than blue until you nail down your process, this issue pops up fairly frequently in the printing industry, I would never blame my customer for it though, usually you see blue on the screen and you end up with purple, then say "welp, gotta change this up!". When given pantone callouts, I usually look at two of my charts from two of my bigger printers to make sure I'm close (I had a pantone swatch many years ago, but it is no more and I didn't feel like shelling out some money when my printer charts were good).

What basically happens is your graphics program says "Hey, this color is Pantone 293C, do you know what that is Printer Profile?" The profile responds back with "No, tell me" and the graphics program responds "Well, you should know, but go ahead and use CMYK value 100/68/0/2 or RGB value 0/71/186, whichever you prefer". This was taken from my Corel X3 pantone palette, now it's of note that my newer design computer with X6 has a different value, (it's using 100/86/16/11 and 0/60/167), Photoshop may have different values as well. When it comes to higher end printers though, the conversation is "Hey, this color is Pantone 293C, do you know what that is Printer Profile?", it responds back with "Yep, I need precisely this amount of ink from these cartridges and I'll get you as close a match as I can to that 293". In actuality higher end printers generally use a RIP that turns the colors into ink calculations, and switches Pantone Spot Colors for the closest possible match that the manufacturer has come up with, some people go so far as to make their own profiles too though.

Most American sublimation printers are small scale epsons/ricohs and use Sawgrass inks, below is taken directly from Sawgrass's site: "Outputting spot colors can be challenging with sublimation as what you see on screen is not what you see on paper or on the pressed substrate. Use of standard color palettes such as PMS (Pantone Matching System) commonly found within graphic applications are not suitable. The same is true for spot colors you may create independently. Sawgrass offers a vast color palette to assist with this."
So basically what they're saying is they've noticed a big discrepancy with the profile matches, and they suggest using their swatches to try to get the proper color. Sounds like you're the customer in this case though, and I'd just throw a royal blue shirt at them and say "this is the blue I want, get me close please", if the don't know how, probably should move on to a different company.

That's a pretty hard question to answer, but the answer is "it depends on the printer".

In the case of sublimation, with Sawgrass inks, I've found RGB is probably the best format to use. Sublimation generally aims towards photos and the like as well, so to maximize your gamut, designs are best done in RGB and then go to the sublimation profile for a CMYK conversion. Many people think designing in CMYK since that is what inkjet printers use will get you the best color output, but by default the CMYK color gamut (AKA the color space/how many colors the printer can print) is more limited and the profile actually will do a bit better job at shifting the colors to get it more accurate and more vibrant than if you were to try designing in pure CMYK.

That's not to say you should be designing everything in RGB, if it's for something like a company logo and the like anything you want to be uniform in color across multiple medias it's best to use pantone. If it's just a t-shirt design, or something that has a whole bunch of colors/effects, I'd say stick with RGB. When it comes to logos you have to look at signage, screen printing, possible pad printing for promotional items and so on, all of which Pantone is the norm and will get you the most uniform result. Sublimation is just kind of the oddball in the situation you're experiencing right now!