Odd behaviour is observed when some applications open maximised on the primary monitor: interacting with the window causes it to jump to the secondary monitor (still maximised).

Different behaviour occurs with different applications, and on some applications it isn't observable at all. I'll describe the behaviour with a few applications.

 - With Files, on opening it (correctly) opens maximised on the monitor the mouse cursor is on. If this is the secondary monitor, it stays there. If this is the primary monitor, then the first time I open a folder (other by double-clicking or pressing enter), the application jumps to the secondary monitor (even though the mouse cursor is still on the primary). Other types of interaction (e.g. opening the menu) don't make it jump.

 - With Firefox, the jump occurs immediately on opening. So you see it for a fraction of a second on the primary monitor, then on the secondary. (Again, if the mouse cursor is on the secondary monitor to start with, it opens and stays there, as it should).

 - With Gedit, similar to above except the jump occurs only on interacting with the menu with the keyboard. So just typing nothing happens; opening the menu with the mouse nothing happens; but press alt-f and it'll jump from primary to secondary.

If any of these are opened in windowed mode rather than maximised (by closing them while in windowed mode then opening them), no odd behaviour is seen.

With some other applications (e.g. leafpad), no odd behaviour is seen.

Mutter and gnome-shell both version 3.6.1-0ubuntu1 on Ubuntu 12.10. The behaviour was also present on 3.4 on ubuntu 12.04. My primary monitor is to the right of my secondary one.