This is really counter intuitive. It seems the most neutral one is R10. Does this mean I add 10 on the red? Will that not increase the warmth?
Yes that is what to do if the R10 image appears most neutral. You are right that adding more red to the image will make the colour tone more warm.
I just made a test with my MP990 that uses cartridges refilled with the
ink set for PGI-x25/CLI-x26 inks. I think this ink set works well with many Canon printers for home use of different cartridge generations and it also works well with HP printers for home use. I use bargain photo paper of brands Sihl and NetBit that were sold by Aldi and Lidl supermarkets in Denmark.
If I print the test image with no corrections applied the print has a green cast meaning magenta should be added. But the viewing conditions affects the perceived colour cast very much. Viewed under an old 60W incandescent bulb and a LED bulb with a 2700K colour temperature the most neutral image is M 10. One 3000K LED bulb shows M 15 as the neutral image and another 3000K LED bulb shows M 20 as the neutral image. A 4000K LED bulb shows M 25 as the neutral image.
In daylight at 10 AM in Copenhagen, overcast which probably equals a colour temperature of 6500 K the test print appears neutral with no corrections applied?? This is also counter intuitive, but I think the reason could be
metamerism which the magenta inks both Canon OEM and aftermarket are claimed to suffer from. Another cause could be that the LED bulbs do not have perfect continuous spectra, but might have gaps in some colours. Ordinary LED bulbs for home use seldom have
Ra or CRI values better than 80.
Professionally special daylight sources with a Ra/CRI value close to 100 in a neutral grey viewing box are used to compare colours.
Maybe it is your test image that is the problem? maybe you will get another result with another test image?
I'm no expert in this. Maybe one of the experts might have better explanations?