Sounds like you have completely misunderstood something and is mixing up two different things.
The photo of a D65 calibrated monitor is used to get custom coefficients for the white balance module. Once that is done, you use color calibration as normal. At no point does delta E enter into it. It’s also explained in the manual.
If you have a color patch target, you can then do lighting/scene specific color calibration, which is when you have to worry about delta E. Note that a simple grey card won’t do for this - you need one of the supported color targets.