Hi,
This is not a feature of what Apple calls "Sync" in Messages.
Basically each device you have has a unique Login to the iMessages servers based on the Serial Number.
The iMessages servers push the iMessages to the devices until they accept.
This is achieved by the iMessages servers effectively "copying" the iMessages until there is a "Copy" for each device.
Then there is not connection between any of them.
What is received by one device is unconnected to any received by another device.
It is best to think of them as different iMessages even though the content looks the same.
So once an iMessage has left the servers it has nothing to do with any "copies" to sync them in the way a Mail Server set up might.
It is more like a POP server in mail being accessed by several devices set to "Leave the message on Server" than IMAP servers.
There are subtle differences in which iMessages show the "Read" or "Delivered" info back to the send based on which Apple ID or iPhone number it is sent to.
That is to say that if your iPhone and Mac are both set to use the iPhone number as a Send and Receive option and the iPhone is set to respond with the "Read" option then if that iPhone is Off Line for some reason the Mac will see the iMessages as it syncs to the Mac but it will not respond with the "Read" info. The Mac will only send a "Read" option if the iMessages is to the Apple ID.
To be clear. In this case "Sync" is only "Display on all devices".
8:22 pm Sunday; December 13, 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