HI,
Messages was born out of the iChat App
iChat used Buddy Lists and these could have individual Statuses set.
One Buddy List remains but only if you have a Jabber account in High Sierra.
The most common is GoolgeTalk or Hangout from Google as Google run a Jabber server.
If you have not set up a Jabber account in Messages then the Status seen with the right click or in the Messages > Menu > Status will read Off Line.
The iMessages account has not Status.
It is either Connected or it is not.
It makes not difference which ID or iPhone number is the "Start New Conversations From" ID
I have the Apple ID set on my Mac and the iPhone Number set on my iPhone.
It only applies when you use the New Message option.
All other Connection use the ID that was last addressed - that is to say if some Addressed you as the iPhone Number then the reply or next outgoing iMessages will be from the iPhone Number.
Prior to High Sierra the out of sequence messages was normally down to time issues.
Realistically you Mac needs to be using Internet Time set in System Preferences > Date and Time and the nearest time server to you.
You also need to be set in the right Time Zone.
If your routing device also uses a Time Server then this should be the same as the Mac one.
However depending on the age of your computer, the amount of Apps open and how they impinge on Processor time you may find that your computer itself is not keeping up.
IF you mouse over individual iMessages you can see the time linked to them.

As you can see my reply in this pic is timed down to the second.
Sometimes a NVRAM reset can help How to reset NVRAM on your Mac - Apple Support as this is somewhat tied to the System Preferences and can be considered low level maintenance.
Having said all that the issue does seem to be reported more in High Sierra so it is likely that some other change is the cause of the issue.
Full sync between all devices using iOS 11 and High Sierra is coming. (it was promised at the start of High Sierra ans we are still waiting)
However this will mean changes to the servers and it might be this work that is causing the issue.

9:08 pm Thursday; March 8, 2018
iMac 2.5Ghz i5 2011 (Sierra)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
iPhone 6 iOS 11.x and an iPad (2)