Also, WB is only one part of the WB control, Tint is the other.
When I shoot tethered I can do an in camera custom WB and it looks good, if I then go into DPP whilst tethered I can re WB that image with the additional Tint control and it shifts, sometimes quite a lot.
But the tint issue in AWB is one I never really did get my head around, if WB just does blue to yellow, then tint, with green to magenta, is every bit as important, particularly for things like stadium gas lights and fluorescent lamps and the multitude of colours they now come in.
Yes, tint is important. The in-camera Auto WB applies both a color temperature and
a tint value. For example, an image open in DxO on my desktop right now and taken in mixed lighting (tungsten with daylight from a large window) shows As Shot values of 4298 K for the temperature and –27 for the tint (a bit green-shifted, the slider runs from –100 green to +100 magenta).
As far as I can tell, Canon's DPP doesn't show the tint value for RAW images or allow you to edit it...but it's recorded as part of the AWB saved in the RAW metadata. RAW converters that are more functional than DPP allow you to view and adjust the tint as well as the color temperature. Just one more reason I don't like DPP...