I just tried that image. The CAT relies on the usual white balance to correct the image to D65, so that the color input profile gets predictable. But for the Sony from that picture, the red white-balance coeff is 2.67, which is massive and probably wrong (most sensors are between 2 and 2.33). If you force a red coeff of 2.0 in white balance module, then retry the color calibration sampling from any grey patch, then it will work.
Problem here is we stack the color calibration on top of white balance and input color profile, so we expect/pray for anything else having been profiled properly.
I got the smell of the red factor issue because cyan is the opponent color.
All the CCT computations there are approximations. The temperature slider of color calibration computes the XYZ coordinates of the illuminant from an approximation based on temperature input. Then the CCT display tries to find the best temperature match from an approximation based on XYZ input. Having only 1 K of error in the roundtrip is actually impressive. And you get rounded to 1 K, so a visible difference of 1K could be an actual difference of 0.5 K.
Don’t even try to compare temperature readings from both modules. Again, color calibration takes an input that is already pre-corrected by white balance and input profile.
Right click on slider, input value on keyboard up to 10.