All the ccp profile is just that ... A profile. It's no different than choosing Adobe Standard, Camera Standard, whatever. In fact, if your camera matches the samples that Adobe used when creating Adobe Standard then if you followed the correct steps there should be zero difference between your ccp dual illuminant profile and Adobe Standard. Since I doubt you have an ISO standard light source to create the profile it's likely the stock Adobe Standard profile is more accurate.
When I saw zero difference between the one I created for my D700 and Adobe Standard I tossed the ccp one.
To me the ccp only really shines when doing studio work using consistent lighting, if Adobe botched creating Adobe Standard for your camera (gets fixed when users complain, so only an issue when a new camera is added) or if your camera is significantly different than the samples Adobe used (I'm betting this is unlikely). Just my opinion though and I'm certainly not fussed if others disagree.
To use the profile do the same as for any of the other profiles you have in the dropdown. Select what you want to use then start editing, starting with WB. To me if the profiles are built correctly WB shouldn't change from profile to profile anyway. Saturation, intensity of certain colors, blacks, whites and contrast should change, but neutral grey shouldn't.