I would just look at the CMYK changes, doesn't mean its correct but considering the subject wouldn't necessarily be out of the ordinary. You just have to analyze the composition to see if it creates any oddities.
A couple of things to think about.
Changing two sliders to tweak colours or correct a colour cast is quite normal. I will often add a bit of yellow and red (= orange) to warm up a portrait a touch.
Moving all three sliders just adds a bit of neutral density to the overall colour correction. You have effectively dialed in 21 units of cyan (-12 on the slider) and 9 units of neutral density (i.e. gray).
Oh
I see that the balancing was done (just?) to the mid-tones. How does "best" work out in highlights or shadows?
As to technical terms, I see that the sliders are moving between the primary colors RGB and their complementary (opposite) colors CMY. In other editors, some similar functions do work best if the adjustments themselves are "balanced". One such function in RawTherapee, the "3-Channel Color Mixer", keeps neutral colors neutral with certain combinations of sliders, even if one actually swaps channels like in IR work.
Getting even more technical, the 3-Channel Color Mixer works just like a 3x3 matrix multiplication and they often benefit in the world of colour transformations if each row of coefficients adds up to 1, or at least the same number ...