Hi,
So you have Messages App open.
However you have also closed (used the red Blob) the main Messages window so that you cannot see any current conversation.
You have the Notification Centre set to Notify on Messages and it does so for incoming iMessages.
At this point you say it opens 4 windows when you click the Notification.
Can you tell what what 4 windows ?
It should only be the Messages main window (Chat window/Interface)
I tried to test this using one of my own iPhones
I picked the one with the same Apple ID and it turned up like synce (no Notification, no sound alert)
I changed iPhone to one that does not use the same Apple ID
I got Notifications and sound but clicking the Notification does not open the main Messages window (I did still have my Buddy Lists on view).

9:24 PM Wednesday; September 5, 2012
Please, if posting Logs, do not post any Log info after the line "Binary Images for iChat"
iMac 2.5Ghz 5i 2011 (Lion 10.7.2)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
"Limit the Logs to the Bits above Binary Images." No, Seriously