After a lot of reading I could answer this myself:
CATs, even the older ones are based on correlated color experiments and
does model the color inconstancy aspects of human vision. Thus it's not
correct to use them for "relighting", but people do anyway as there are
no other established standar
I've the author of DCamProf an open-source camera profiling tool that
can do DCP and ICC profiles. I use LCMS2 for CAT02 and various other
color management stuff.
Recently a question came up regarding how calibration in light
different from D50 should be handled. Let's use StdA in this example.