Most offset printers are very accustomed to working with colour values to achieve a result on their press and make the assumption that you can work in the same way with a digital device. I have seen this many times, and have great respect to the printers that understand colour that well, although unfortunately the ink & print technology in ALL digital printers does not react the same as a press with film or plates will.
If you took 3 different digital printers, unfortunately you would have 3 very different coloured Cyan, Magenta, and Yellow ink sets. Not only that but because the media these printers are laying ink onto has a specially formulated coating to receive and hold this ink, each machine will produce a different reaction to the same colours. This means that by not using custom profiles and adjusting the CMYK file values as you could do if you were making film or plates will not work on a digital printer or proofer. If the colour of Magenta is different from one printer to the next, then by simply adjusting the density curves will not achieve the same results between these machines. This also explains why digital proofers mix additional colours into what could seem incorrect as a primary colour.
A typical example of this is in yellow, where additional colour are sometimes visible on a digital printer making it appear dirty: this comes from the problem that the actual colour of the yellow ink is different to what you have asked it to print, and the profile tries to match the same yellow by mixing in other colours in very small quantities. Sometimes in a profile that has a limited gamut this can give an undesired result by making primary colour appear dirty, but on a quality media & profile combination this will work for you and not against you.
I once worked along side an offset printer that created a manual calibration curve in the rip software and used no colour profile (as you would on a press) and then tried to produce canvas prints with very specific colour requirements. I respect this person’s ability very highly, but he was not able to get a satisfactory result in doing this. I then used measurement equipment and software, and calibrated his rip and produced a customICC profile for his media/printer combination, and nailed the result that he was unable to get otherwise.
So why was this the case? By adjusting the curves on his digital printer, he was able to maintain very clean primary colours, but by the simple fact that each colour curve, is a curve. When you move the curve in one place, it affects the colours around it. In an ICC profile, each colour is it’s own unique calculation and has no relation to a similar colour that it would otherwise. Each colour is uniquely considered in relation to LAB (or how it should look to the average human eye after it’s printed) from an ICC profile.
If you have questions on this topic, unfortunately it’s too advanced to explain in full detail on this web site, but I welcome you to contact me to discuss it further.