I use Mate on Ubuntu and I don't run compiz. This fix is specific to Mate without compiz.
Sometime in the recent previous Ubuntu versions, Unity (and other things that depend on the gnome libs, I guess) implemented window auto-maximizing when their upper edge touches the top of the screen (or the bottom of the top panel). This may also affect the left and right edges of the screen, but it was always only a problem for me with the top edge.
To fix this in Mate:
System > Preferences > Look and Feel > Mate Tweak
and uncheck enable window snapping.