The JPG image embedded in the NEF file is just one way of interpreting the raw information to make a final picture. It is the automatic conversion done in the camera. This is the conversion used to show you what the picture looks like on the monitor in the camera. They have to pick something. Nikon also encrypts the information so that you can't do the same conversion without the decription key.

This in-camera conversion does take the ambient light color into account, so it's usually not too bad, but it is certainly not the single right answer. The automatic process has no idea what parts of the picture are important to you or what you are trying to show.

Some software may do its own default conversion from the raw data, sometimes just because it doesn't do the decryption. In any case, the JPG picture is just meant as a quick basic way to show you the picture, not as your final picture. It therefore doesn't matter what the camera did or what various software programs do. They all fill the purpose of showing you the picture. Beyond that, the JPG picture is irrelevant, as is any other automated preview derived from the raw data. Ultimately you have to decide what you really want and steer the conversion process accordingly.