The point is, if you don't learn to make prints yourself, you first need to know exactly what you want, and then find a lab which offers CUSTOM PRINTING you can communicate well with. Yeah, you can keep rolling the dice hoping an automated printing device will land on target once in awhile; but the statistical odds are always against gamblers.
So you not only need a commonality of relevant terminology with any such service, but a commonality of how the end result is assessed. The industry standard has long been 5000K using a high quality light source (which all common inexpensive LED and CFL sources are NOT). You can still have the color balance tweaked to match specific other display lighting circumstances, but need to start at a common denominator point. These are just some of basics. Otherwise, it's the wild West, and anything goes, beyond your control.
And to anyone with a halfway trained eye, whether painter of photographer, or dye or pigment engineer, cyan and blue are totally different animals. You can't even correctly operate a colorhead without recognizing the distinction. Yes, in between that primary and secondary, are all kinds of intermediates. But one should at least learn how to distinguish the main slices of the pie, and when they're on target or not. That what things like high-quality standardized Color Checker Charts are for, along with standardized lighting for evaluation. Take a photo of such a chart under specified Kelvin temp and correct gray scale exposure conditions, submit that, and see how the print compares. Objectivity first saves a lot of headaches subsequently.
[...] superior quality printing has always demanded some extra steps. The only difference these days is that the same kinds of tweaks are now more often done via digital workflow, inheriting many of the same terms including masking, than their direct graphics and darkroom precedents using film-only methods. But both are possible, if not by the photographer themselves, by some service willing to do it for you. But that goes beyond what any mere rote machine sensor and software can do by itself, and will obviously cost more per print too.