Nikon's Capture NX is a proprietary software and the profiles you create with it will only be usable by your camera firmware and Nikons software. In the same way if you create a profile with the Adobe DNG Profile Creator it will only be used with Adobe products.
Expanding on the answer from DdeGannes, none of the profiles (factory or custom) from Nikon (or Canon or others) are read by Adobe's software. (No third party software reads them.) Adobe does have approximations of the factory profiles in the "Camera Calibration" panel.
The reason you see the custom profile in the initial thumbnail and view is that these are initially created from the JPG preview inside the raw file. The JPG preview and any JPG image created by the camera will have all the camera settings baked into the JPG image.
Thanks guy for the information. It pointed me in the right direction to learn how to make custom Adobe camera profiles that mimic the Nikon custom profiles I made.