I think what you would like to do is device dependent, meaning even if you set the color scheme on the PC it will reset on xbox, because the setting is not saved on the controller, just on the PC. Because of this, setting the color, I guess, could be possible with an app from the Microsoft store: Razer Synapse for Xbox, although that is for Razer Wolverine, maybe it will work with yours too. The razer synapse software, that you use on your pc is for windows only. The app from the store though should do the thing. I never used razer products, but have an illuminated keyboard, that has a separate button for setting the light. In which case, the settings are actually stored on the controller, keyboard, etc.. Maybe check if such a button exists on your razer items?

Razer Synapse allows you to assign the side buttons to either clutch or toggle through sensitivities, which for the Deathadder 2013 goes from 100 DPI to 6400 DPI. Here are some pictures to clarify:

The list of profiles is alphabetical, and the last item in the list is always chosen. Just put a Z in the beginning of the profile which you wish to be the default.