Yup, need pictures. Just for some wild guesses... It could be set for white balance bracketing. The odds of your friend having that also set are slim though. Or maybe you were you shooting indoors under florescent light? Depending on shutter speed, you can see various colors from the florescent light as caught at the different stages of each ac cycle. Some pics should narrow down the cause.
Auto-WB can cause color differences; especially when combined with auto-ISO. If you move during continuous, every shot could be calculated differently.
Exposure differences could look like color differences too. It's even possible the lens is slacking. I currently have it with the big Tam which leads to about 1/3th of a stop difference between shots during continuous.
Btw; if you and your friend both have the same issue, it is unlikely the problem is the D750. It's more likely some settings are wrong.