Hi Darin,
FastArtist has built in color profiles that are usually very accurate. The color profiles were developed over countless hours to try to ensure that what's on the computer screen will match exactly with the shirt.
In my own experience, at least, color matching is excellent and, when colors are a little off, it's easy to make adjustments to get exactly the colors you want.
We have a support department at Equipment Zone that can direct connect to your computer over the internet to check that the settings you have in your software are correct. It may be the case that all you have to do is make a minor tweak like saving your artwork in a different color mode (RGB, not CMYK) or making some other small adjustment in order for the printer to print out the same color that you're seeing on the screen.
Please give us a call! We'll be happy to help you get that perfect turquoise.
-Alex