Should iMessage not be silently updating my phone when I'm at my Mac? I've been using iMessage with a friend of mine over the past two days. When I get the message on my Mac, I also get the message on my phone. That's great, BUT why all the alerts and buzzes on my iPhone? It's very annoying.

Should iMessage not see me receiving the message on my Mac and silently update my iPhone?
No, it doesn't (yet) have any methods of muting alerts on other devices even when it has reason to know that the alert has been read etc.

I'm sure that it will arrive soon, but as it stands every device is treated independent of each other with regards to notification settings, or to put it another way, notification are "device independent", and you are waiting for them to be treated as "notification independant", as it were.