The push notifications come through to your phone even if you are currently using AIM on your desktop machine. I have had the app for only an hour and have sadly had to disable the notifications since it was driving me nuts.
I have the same problem. I had a friend send me a message which got pushed to my phone. When i jumped on my computer to chat, it still sent the messages to my phone. Was very annoying. Any one have any clues on how this can be changed?