I would try disabling iMessage on the Mac, Quitting Messages, maybe even restarting the computer. Sign out via Messages > Preferences > Accounts. Then sign back into your iMessage account and see if the issue is resolved. If not, I would try diabling iMesssage on every one of your devices, then sign back in, in hopes that it will be "reset."
You could also try deleting all conversation history on the Mac. If none of the above works, it might be time to delete some plists and try to get Messages back to its original condition.
Let me know if that helps!
The "Fix" Apple list in the document about the changes in OS X 10.8.3 refers to issue with the iMessages order on waking from Sleep.
It does not mention anything about the iMessages being out of order if the computer has been Shut Down and has just started up and Messages app launched.
Nor does it say anything about any iMessages appearing out of order at any other time.
Realistically people report mixed up messages in all three of these scenarios.
Your issue seems to be more about the iMessages actually Syncing in the first place and not to do with it being out of order.
I would also try a PRAM reset.
Shut down the computer.
Restart it holding down Apple/CMD ( or ⌘)+ALT( ⌥)+P+R Keys until you have heard three Start Up Bongs.
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