<<This photo was printed on a greeting card and the client says the skin tones printed too red. I asked the printer (
www.psprint.com) to reprint since the exact same TIF was printed beautifully by the same printer 6 months ago.>>
This happens all the time. It could be that their cyan ink was not up to par that day? It happens.
<< They say my values are way too high in magenta and yellow and won't reprint. :-<>>
These readings are too high for press (magenta and yellow). But the image brought into an image-editing program, does not reflect these readings. The image when brought into an image-editing program. The values seem to be not far off. Settings I use: (colorspaces) RGB: sRGB....CMYK: SWOP inks, custom dot gain curves...... which I set with a GCR setting: light, 85% black ink limit and 300% total ink limit. I don't use the default cmyk profiles of P.S........... With my settings (flesh tone readings), the cyan is half the value of the magenta and yellow..... In fleshtones you want the value of cyan to be 1/3 to 1/5 the value of the magenta and yellow, sometimes it can be 1/2 (monitor as guide). This depends on skin type. The magenta and yellow should be equal, if not, the yellow will be higher. When reading the numbers its more important for the ratio values than the exact readings. In a highlight. Shoot for a setting of 5,2,2 setting. Shadow.... 80,70,70. Neutrals... The magenta and yellow should be equal and the cyan higher. 6 to 7 points in neutrals. But this also depends on what your printing to (web press, sheet-fed press, ie.... how their running it) Their's a lot to this. It's not,.......unlike printing to the internet or an inkjet printer. You have different stock, inks, presses for output, lpi. In RGB....equal values will always be neutral. CMYK is different. A 50% black ink (K) can be made with cyan,magenta,yellow ink as well. You have to look at it as: what you see on your screen, take it with a grain of salt. Because the screen is light-emitting and a press are inks. You can come close.....But a monitor is not a press or it conditions. Do you remember "Press Ready" a program that was for (rgb to cmyk) printing? I don't think you can get that program any longer.

One example is: you can oversharpen on screen and it will print fine on output. Even for an inket. The screen will look oversharpened. You have a lot with monitors......LCDs' fall into this as well....... Dot pitch (spacing between pixels) is only one of those. I have an electronic-engineering background from college and this helps to understand the scientific part, but in real world printing this is far from it.
I have gone to the web site you posted and quickly gone though it. It "does" state you must send your files cmyk and the only help they give you is to "convert to cmyk". Well.....their are many cmyks'. Do they mean P.S. default (in color settings) for press? What kind of cmyk profile in P.S. do you use? See, this lets them off the hook,
if your files do not print the way intended. Cause "you" did the conversion. But. I would ask then. Something like. What is your total ink limit? Knowing dot gain helps as well. As well as any other info. can be supplied. Sometimes the person who has to supply the file is left with nothing to go on. So use the above as settings. And use 17%-20% dot gain. Get a proof. If your running quantity. To see how it prints. Then correct from there. Using curves....if not use the method you best know how. Doing the conversion is one thing. Getting the converted cmyk file looking close to your rgb is something else. Their are ways, but beyond the scope of conversions. If they want your business. They should help you with this. If not, maybe they have more business then they can handle.
On the file there is an issue of neutral, the white tee-shirts are not neutral. You can correct with curves or levels...... What I would do is apply the green channel into the blue channel (darken mode_100% opacity) with the apply image command.
<<My monitor is calibrated to the printer's standards. It's shot in sunset, partially in shadow and the skin tones are middle eastern, so it should be darker than caucasian.>>
While a calibrated monitor is great to have. Even if they give you a target for their standard (closed-loop, their using). Its better to have: see above.
<<It's shot in sunset, partially in shadow and the skin tones are middle eastern, so it should be darker than caucasian.>>
Make the cyan 1/3-1/2 ratio to the magenta/yellow. You can correct using curves or levels. What I would do is apply the green channel to the red channel (darken mode_20% opacity.. adjust the opacity if need be). Looking at the file is not as bad as those numbers were first given.