Hi,
First Mac starts at 7:30am, the second at 8:15am and the third starts at 9am. There is enough time for the network/server.
I was thinking of several people starting at around 9.00 and then all turning their computers on "at the same time".
I tend to come home from work and turn on three computers after I have eaten.
Later my son will start up his X-Box 360
If I happen to be starting up Messages when that happens I can get distorted figures.
However three Macs spread out like you say should not be an issue.
The issue might be related to the My Card in the Contacts App.
iChat used to have issues if the Address Book did not identify the My Card properly.
This would also be an issue for the Bonjour Buddy list as it calls on the Contacts > My Card as the Buddy name for your computer (the same on the Others to be your "Buddies").
Now I have issues with iCloud, Mail, FaceTime, Language Settings, App Store, Shared Devices, Messages, …
This could be a Font Issue.
Use Font Book to check.
Certain Fonts are needed by the app to function.
In Tiger iChat would not start if Helvetica and Lucida Grande were missing or turned Off (or corrupt).
Helvetica is needed to display the title of the Window.
Lucida Grand is the Font for the Group titles in a Buddy list.
I am not fully up to date with which Fonts Mountain Lion may be using for these things - Menu Bar and titles of windows look as they have always done and the Buddy list seems to be the same with regard to Group Titles.
There have been conflicts in the past with Helvetica Fractions being installed.
9:38 PM Wednesday; March 27, 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