Hello and thank you for your question, I look forward to assisting you today. Just to make sure I understand your question; are you transferring photos from the Nikon to your phone and computer?
There are many variables that can cause this. Each device you view your photos on will use a different video processor, and each monitor will also display the colors differently. Do the colors look better on the computer than on the phone?
Still with me?
Is the computer photo edited?
I haven't looked over the D800 manual that close. Is it capable of shooting in RAW format?
Is that how you shoot with both camera's?
Looks like the D800 is shooting a little red to me. How long have you had it?
So the only time you see a color change is when you download the photo to your phone?
How do they look when downloaded to a different phone?
Do you email the photos out as an attachment from your computer directly to individual phones? If so, they will be compressed and you will see some loss of resolution.
Have you considered using a photo analyzer to compare the original against the uploaded one just to see if there is any difference in the data?
I have used one or two in the past just to see what I could find out about a photo. They range from the free to very expensive depending on what you are trying to accomplish. Here is a LINK to one of the free versions.
Here is a LINK to a not so free service.
This one might be just what you are looking for? LINK
I will be going off line for a short time but I will be back with you as soon as I can.
I don't think it is on the computer end, but you may want to check the calibration of your monitor if you haven't already?
Here is a good place start. Monitor Calibration