But how is this achieved?
The system is not perfect. I personally do not like a lot of dumb decisions they made. But the basic idea is that they have:
A catalog of consistent printed colors.
A set of base colors and the formulas to achive the derivated colors.
The base colors have some specific values on colorimetry that are repeatable by diferent manufacturers of inks.
I assume there are no "Pantone Inks", right?
Yes and no. Pantone is the system to have a consistent color. Then, diferent ink manufacturers make a set of base inks based on the specifications.
So a manufacturer "HappyInks Inc." make an ink, for example "Pantone Reflex Blue"
Printers then go to the formula guide to find the recipy for the colors on the catalog, and go and buy from "Happy Inks" the basic set of colors.
They combine "Pantone Reflex Blue" with "Pantone Sunrise Yellow" in some specified proportions (from the pantone formula guide) to achive "Green XXXc".
If you are going to need a lot of ink of one specific color, the printer do not mix the base inks themselves, but ask for "Happy Inks" to make them some kilos of the ink (based, again on the pantone specifications).
The quality of diferent brands can be more or less accurate. Besides that some characteristics of inks can differ because some could be oriented to silk print, or textiles etc.
the printer needs in RGB.
This is a biiiiiig mistake.
RGB is not by any means an acurate color reference. Either your printer is lazy or he is simply using some kind of digital print (but still is ignorant(*).
You need to include a RGB profile. Either sRGB or Adobe 1998 but you need to design using a CMYK profile, which obviously you do not have. So ask for which one is more suitable for that.
If they have no idea or say something like "It does not matter" use one according to your location. SWOP 2, Fogra, Gracol, etc.
Will the colours vary too much if using a Pantone - RGB convertor?
If the project is on flat inks, the proper step would be that you deliver a project in Pantone and let them do the conversions, so they are responsable to match the color the best way possible.
This is why I say they are Ignorant. (*) They ignore what is the calibration of their own machine. They should profile it and give you some clues on what "generic profile" suits them the most.
This does not say much. Are you printing rolls and rolls of fabric? Are you printing a Tshirt on a digital medium, like a logo for a student party? Are you using silk print for the campain for a company?
An Aditional note
will the colours vary too much
Colors vary for a looooooooot of reasons.
My clasic example, grab a water based cyan marker. You have a specific ink one and only one.
Now go an paint everywhere you want. A news paper, a magazine, a window, a white towel, toilet paper, your hand.
See? The exact same ink vary a lot. This is why you must have an output color profile, so this gives the internal conversions and calculations to have the most acurate color possible due this combination of factors, which color on which medium.
This is why the printer should be responsable for the color conversions.
Aditional Note 2
There are some conversions from pantone to cmyk and rgb... Ouch.
This are very specific conversions. On some "ideal" situations.
More or less how an ink will be printed following exact specifications, for example a CMYK: type of paper, type of inks, controlled ammount of them (densitometry), etc.
For an RGB one they assume a calibrated monitor, Correct gamma, correct temperature, sRGB profile. But again this rgb simulation is for output for a web page for example, not as a printable file.
Spot color (Pantone), or Color selection (CMYK)
Depending on the type of design you have the choice to print in either of this 2 color modes.
For example, a design with gradients and diferent colors most likely needs to be printed in color selection.
But some other type of design needs to be printed with spot inks, or direct colors, this reduces costs and aditionally allow the colors to be consistent