Hi,
Try it this way.
Ensure the iMessages app is disabled in the Messages App and in the Preferences > General Section the items that reads "When I Quit, set the Status to Off line" is ticked. This last part only effects Accounts in Messages that have Buddy Lists (not the iMessages one which needs turning off separately.
Quit the App so this takes effect.
Then in FaceTime (it also uses IMAgent) set that to be Off in it's Preferences, Quit the app.
Then in ~/Library/Preferences find and move to the Trash the com.apple.imagent.plist
To access the ~/Library use a the Finder > Go Menu whilst holding down the ALT/Option key and selecting the Library, then navigate to Preferences.
Then Quit the imagent app in the Activity Monitor.
The item should not, in this case, reappear at the top of the list as the two apps that us it should be turned Off.
Then Restart the Mac.

8:42 pm Saturday; February 28, 2015
iMac 2.5Ghz i5 2011 (Mavericks 10.9)
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