My applications have been abducted by aliens

Well... not quite I was just wondering why some applications disappear or stop launching after deleting or ejecting the *.DMG. For example, Mozilla Firefox and Second Life do NOT disappear, even if you reboot your Mac/eject the *.DMG on the desktop/delete the *.DMG in the folder it was downloaded.

But others, such as Transmission, disappear. It won't allow me to eject the *.DMG, if I delete the *.DMG the application won't launch anymore, and if I reboot, it does not show the application's icon in the dock anymore, unless I launch it, in which case, it takes a few seconds to find the *.DMG.

Any explanation will be much appreciated, thanks in advance!

And how do I install the app? Don't I double-click it? Because that's what I did, EXCEPT for the fact that I didn't "download" it ("Save as..." in Firefox), but simply ran it ("Open with... "). But that's what I did for many other apps. Why don't these ones want to work?

Oh, thanks a lot. I thought I've only got to copy the application into its folder if I'm prompted.