Hi
No the screen doesn't rotate automatically on Mac OS. In System preferences there is a possibility to rotate a connected monitor any degrees you want. I need to rotate the screen 270 and THEN I rotate the monitor myself - it's on an adjustable monitorstand.
So if you imaging a 16:9 monitor, where the menuline normally is located at the top on the long side, then the menu line is now on the short right side of the monitor, and then I rotate the monitor and everything I perfect.
So I need to address the System Preferences/Screen for the leftmost monitor in my set-up.
Hope it's more clear now!