Question re: opening Disk Image (.dmg) files

I'm perplexed. Under previous OS's, up to and including Snow Leopard (10.6), whenever I used to double-click a .dmg file that I had downloaded to my Desktop, the file would mount right there on my Desktop. With Mavericks (OSX 10.9) it still does so on my wife's 2011 MacBook Air. Files from disk images have always mounted on her desktop, using all OS's. However, starting with Lion (10.7), continuing with Mountain Lion and now with Mavericks, on both my previous 2006 iMac, and now my late 2012 iMac, .dmg files are expanded to the root level of my Finder.

I find it a pain in the rear to have to navigate to the Finder to locate the file, and I cannot understand why this happens on my machines but not on my wife's.

I've tried launching DiskImageMounter (in /System/Library/CoreServices) to see if there is a preference I could set to have the expanded .dmg file mount on my Desktop, but no go. Trying to launch DiskImageMounter results in that app's icon flashing, but the app itself does not appear. I even tried modifying that app's .plist files (in DiskImageMounter/Contents/etc.) with Property List Editor, but I saw nothing that suggested an assigned destination for mounted .dmg files.

Can anyone shed light on why the behavior on my computer now is different from what it was under Snow Leopard-- and what the behavior is now, and has always been, on my wife's computer, using all OS's?

Better yet, can anyone tell me how to change the destination of expanded .dmg files on my computer?

Thanks in advance.