Both the Mac in Messages Beta and the Phone in Messages should be using the same Apple ID.
All old messages involving either the Apple ID or the phone Number should be deleted or Forwarded (if you want to keep them) and then deleted from the Phone.
This allows the Settings > Messages > Received At > Caller ID info to by synced properly.
When you have cleared all message first there s a link created between the Phone Number and the Apple ID so that all Messages the iPhone receives are synced with Messages Beta.
If you do not clear the Messages on the Phone (Most likely iPhone Number to iPhone Number) then these can seem to remain "private" and outside of the sync process.
Messages beta on the Mac is just that, A Beta.
This mean that it is not perfect.
There is some anecdotal evidence that the servers for iMessages cannot always keep up.
If you turn On Messages Beta when you get home, it will try to sync the Messages the iPhone has had.
You may get new iMessages from your contact out of order with the "history" making conversation a bit difficult. (it seems you can send replies out of order as well)
Please, if posting Logs, do not post any Log info after the line "Binary Images for iChat"
iMac 2.5Ghz 5i 2011 (Lion 10.7.2)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
"Limit the Logs to the Bits above Binary Images." No, Seriously