I may be misunderstanding :) The colours in the LightMix act as multipliers to the original light colour (as do the intensities). This means that white, intensity 1, in the LightMix controls gives you "the same colour as the original light source".
If you set the light colour in the LightMix controls as well as on the light, then you are changing the colour of the light (now it's original colour * original colour). This is unless you mean "Set colour in the CoronaLight and leave LightMix white" vs "Set CoronaLight to white and set LightMix to the light colour" and those are giving different results?
I wasn't aware that the LightMix colors are multiplied by the original colors. But in any case, the color displayed in the dialog boxes for selecting a color should match (or this is my understanding) and they do not. For my tests, I always start with lights that emit pure white (255,255,255 RGB). I then tune the color in LightMix VFB using the color picker dialog box used to change the color (let's ignore intensity and assume it is left unchaged at 1.0 in the LightMix LightSelect). Then I try to transfer the tweaked color settings from the LightMix VFB LightSelect color picker to the actual light source using the 3ds max modify panel (direct light color entry color picker dialog box). Of course I would then reset the LightSelect color to white so as not to impact the light source further, but let's ignore this step for the moment.
So, when I do this and plug the HSV values from the LightMix VFB's dialog box that pops up when you click on a color rectangle for a particular LightSelect element, the resulting color in the dialog box that I am entering into (the one from the 3ds max direct light color entry dialog box) does not match even though the HSV values are the same. This should be fairly easy to reproduce:
Create a single CoronaLight light that is pure white and has intensity of 1.0 - the most trivial light source. Create a light mix and light select for this light (environment excluded). Do a render and tweak the color of the light in the VFB to some saturated color like say mid brightness lime green at the end of the render. Then try to modify the color of the actual light source (which is currently white) to match that of the LightSelect element for it in the VFB. Have both dialog boxes open (the VFB LightSelect color picker and the 3ds max modify light panel direct color picker) and match the HSV values between the 3ds max color picker to the VFB color picker. Do the resulting colors look different (in lightness and perhaps saturation) when compared by eye between the two dialog boxes?