With AIM running, right click on its icon in the dock. In the menu, hover on "options" and see what is selected. If it specifies a desktop, it will only open in that desktop. If you don't want it to do that, you can specify either "None" or "All Desktops". If you specify "None', it will open in the desktop you are on, but will not be visible in the other desktops as you swipe over to them or select them in Mission Control. If you select "All Desktops", it will again open up in the desktop you are on, but then also be visible in any other desktop you may swipe to or go to in Mission Control. This should fix your problem.
Another possibility is that you left it in full-screen mode when you quit it. If you open an app that you had left in full screen mode, it will go to full screen mode when you launch it and go to its own desktop. Taking it out of full screen mode before quitting it will allow it to open in the existing desktop next time you open it, assuming you don't have it opening in its own desktop as described in the previous paragraph.