App windows move spontaneously on display wake (2 monitors) - OS X 10.8.3 OS X 10.8.3
Mac Mini Late 2012, 2.6Ghz quad-core i7, set up with 2 displays, like this:

     Thunderbolt Port          HDMI Port
     /*****************|------|**********\_______________
    |                  | Mac  |          |               |
 ---------------       | Mini |          | DVI Display   |
 | DVI Display |       |------|          | (2nd monitor) |
 |   Primary   |                         |_______________|
 |_____________|


Problem: When I "display sleep" the system (by moving the mouse to a hot corner, to sleep just the displays, not the entire system) -- 



on display-wake, all windows are moved back to the primary window.

I.e. if I had, say, a Mail.app, a Finder, and Preview.app window open on 2nd display, then I put the display to sleep, wait 10 seconds, then wake the displays, all the windows are moved to the Primary display, even though the 2nd display's desktop background shows up normally &amp; simultaneously w/ the Primary display. 

It's as if the 2nd display had been physically disconnected &amp; reconnected from the Mini each time.

Here's why I don't suspect any software or preference issue:

The system is booted off an external SSD running OS X 10.8.3. This exact same SSD was previously used to boot a 2011 Mac Book Pro (model ID 8,2), connected to the same 2 displays, and running in closed-lid mode, and this problem did not occur.

The only differences are in hardware:
a) Now using a late-2012 Mac Mini 6,2 instead of a MacBookPro8,2 as the CPU.
b) 2nd display now attached through an HDMI --> DVI converter dongle. Previously it was attached through a Newer-brand USB --> DVI adapter.

Another bit of info -- if I quickly sleep-wake the display, before the display has a chance to actually complete its "go to sleep / power off" mode changes, the problem does not occur. Only happens if I let >5 seconds go by, long enough for the external display to go to sleep.
I'm guessing the 2nd display is not an Apple display.  

I believe what is happening is that the display is, in fact, going to sleep, but in such a way that the Mac thinks it has been powered off.  

Replacing the  HDMI --> DVI converter with an Apple Thunderbolt --> DVI converter is your best bet at fixing this.