mouse reverse scrolling and not-Apple mouse

The mouse certainly is compatible. It is a mouse, after all.

What perhaps is not compatible is the proprietary software, if any.

I don't know what features that software provides, but if it does not work, I am sure that the mouse itself can work with basic functionality - the left and right buttons and scroll wheel should just work with the system without requiring any software.

So if there is some proprietary software and it is not working, I would uninstall it and try to use the mouse just like that.

Or perhaps there is some updated version?

No, you do not have to have an Apple mouse.

FWIW, I just connected a no-name mouse to my MBP, and in System Preferences->Mouse, I can change scrolling direction just by checking or unchecking this box:

I did not have to do anything, and this is just an old pc mouse. Notice it says nothing about the particular mouse, but it works, and immediately, too. No need to logout, restart or anything. Just change the box at will.

You may want to try that. It should work.