Humm,
So the iPhone receives them in a timely manner.
The passing to the Mac, which would appear to be on most of, if not all of the time, seems to be the issue.
The fact the Messages app shows them out of order but that they reset when the app is restarted suggests that the Mac as a whole would appear to have time keeping issues.
There could be reasons for this:-
1) in System Preferences > Date and Time the Automatic Time Server is not On
2) there are many apps open or possibly one or two that cause heavy processor use.
Symptoms might include seeing the Spinning Beach ball and having to wait for apps to do something.
Check with Activity Monitor (Applications/Utilities) to see if any internal Processes are also using high levels of CPU time.
Whilst unlikely, any time setting in the router might play a part.
Your routing device can normally be accessed in a Web Browser (with the User Name and Password)
Many have a similar time setting such as the one on the Mac about keeping the time as many data packets need time stamps.

7:35 pm Friday; August 24, 2018
iMac 2.5Ghz i5 2011 (Sierra)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
MacBookPro 15" 2016 (High Sierra 10.13.x)
Mac OS X (10.6.8),
iPhone 6 iOS 11.x and an iPad (2)