HI,
Messages has a support app called IMAgent.
It runs in the background as soon as the computer is started.
One of the many things it does is "listens" to those accounts that can do Off Line IMs or iMessages.
What it does when you get a message coming from one of these sources when the app itself is shut down is start up the app and also "Notify" you.
In Messages Menu > Preferences > General Section you can undo this feature.
There is a Line about "When I quit, Set my Status or Off Line"
This will stop Off Line iMessage creeping through and opening the app. AIM Off Line IMs are also stopped.
Jabber accounts vary depending on whether the Server used can Save/Store Off Line Messages.
AIM Screen Names have a separate function that can be turned Off at an AIM web site
This works fro AIM registered names and @mac.com names from Apple.
As @me.com and @icloud.com name need the dual login to Apple and to AIM to then allow AIM to "read" the password you cannot login to the AIM Settings page.
9:43 PM Sunday; April 14, 2013
iMac 2.5Ghz 5i 2011 (Mountain Lion 10.8.3)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
Couple of iPhones and an iPad
"Limit the Logs to the Bits above Binary Images." No, Seriously