As also stated by the user "bkidwell" in the comments of this guide:
The Compiz "Place Windows" plugin is very buggy. If the "Smart" placement method is chosen, then the movement of a window to another desktop (for example using strg+alt+shift+arrow-key) is very glitchy and doesn't work or the window is moved somewhere else then you want.
I also tried the placement method "Pointer". With this the movement of a window does seem to work, but when switching between desktops, sometimes the windows get moved (without command to do so) inside the desktop inside the target desktop.
Another Mate + Compiz problem is that the context menues sometimes stay empty at first, and only when you move the mouse over them the options apear (because they have to be redrawn because of the hover effect)