I previously had my D800's set to sRGB because setting them to Adobe RGB created a greenish cast (the usual non-color managed look) plus it didn't matter in my workflow which setting I had them on. It was easy to see the difference on the cameras LCD monitor by keeping everything consistent and switching the camera back and forth between the two color spaces. The actual photos looked the same on the computer - it was simply the LCD monitor on the camera that was off.
With the updated firmware version, I see no difference now when I switch color spaces on the camera. The resulting images look the same, so I would say the firmware update worked.
You haven't mentioned whether it's strictly the LCD display that shows a greenish tinge or if you see a problem with the actual images. If it's the latter, it may just be a white balance problem. Open shade and a brick wall, when coupled with auto white balance, will certainly give green tones. Interior light in a building can also create green tones, and auto white balance will only correct that to a small degree (more on Auto 1 than Auto 2). If this is definitely your problem, putting a grey card in one sample shot and using it to correct white balance for your other images should solve it. Similarly, finding something neutral-toned in your shot and doing a white balance correction on it should fix the problem.