Hi,
There seem to be several things going on here at the same time.
One is the differences between the Devices Sending th iMessages, which ID might have been used if you Started the chat compared to which devices at the other end is the receiving ID and whether that was addressed.
Add into that mix the fact that Apple said iMessages would be fully sync-able across all devices in High Sierra (they didn't actually say when in High Sierra) but it does mean changes to the Servers and the way iMessages are delivered to do this.
For example of the first bit.
My Mac is set to Start New Conversations From my Apple ID. My iPhone is set to start them from the iPhone Number.
Neither is set to actually Send Read receipts.
However If ON my Mac's version will give a Delivered response to people that Addressed the Apple ID
The iPhone will only give the "delivered response if it was the iPhone Number that was Addressed.
This is despite both IDs being Receive At options on both devices.
As I turn Off my home computer when I am not using it the iPad I have that also uses the Apple ID as the login ID does not respond to item Addressed to the Apple ID as it was logged in later. (It seems the Servers know when sending to Sync devices)
If your Chat shows ID changes in the centre where the Time Stamps also get put then it is likely that your contact is changing the Device they are responding from rather then changing the ID that is responding.
Your iMessages are responded from the ID that was addressed.
SO if the iPhone Number was the ID used to "call" you then your Mac or iPhone will respond as it it is the iPhone.
The Setting for Start New Conversations From does not Override this and is also separate from the Delivered and Read responses.

8:10 pm Sunday; February 11, 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)