Been there, done that 
That issue will be there - potentially - if you had simply rotated 1 of your screens!
If you look at the config file monitors.xml in ~/.config, you see there is an entry in there for EACH monitor combination that you use - or have used! So when you boot up, it compares the set of monitors it has currently found connected - including the orientations I believe - then uses that config entry to set which is Left/Right/Center, which is Primary, etc.
Seems like a great idea, and it would be except ... when it doesn't find an entry for that combo, it CREATES one! Now clearly that's necessary on the very first boot of a newly installed OS (else you'd never have a display to use ), but in all other cases it has the potential to make an entry that you don't want, because you were, say, just connecting to see if it worked ... And on top of that, when you close down the OS it saves the current settings regardless of how messed up they may be, if you have entered the Displays applet!
I use 2 Dell's (next size up to yours), with 1 each in portrait and landscape, plus the laptop's own monitor. [It's a re-purposed Gaming laptop, so has a nVidia card.]
What I had to do in the end was make a copy of ~/.config/monitors.xml and then work my way through identifying the ones I wanted and deleting the others/rest. Non-trivial, but can be done. [It may be better to save a copy and blow away the .config version and build a new one, if you have lots of 'bad' configurations to sift through as I had.]
Once you have a clean'ish file then you can make your final edits and SAVE A COPY. Oh, and remember to preserve it somewhere else when you do a clean OS install, 'cos you're going there again. 
FYI, the problem is upstream of MATE. I know because on 17.04 there was a further issue that the combined display size is incorrectly calculated if the portrait monitor is in any position other than the far right. This was corrected on a later release subsequent to my bug report (1723238). The fix had to be done upstream. I believed that it was fixed in 18.04 - not sure as my test systems only have 1 monitor. But it sounds like you are still experiencing the same problem as I was in 17.04. 
Perhaps there is a further problem with >1 portrait monitor? You may have to: put all monitors in landscape, get a auto-generated monitors.xml, then manually edit to change them to portrait, along with the required arithmetic changes to reflect that a rotated HD monitor is 1024 x 1920 not the other way round.
I feel your pain, but have done it twice (that's how I know you need to save a copy elsewhere before a clean OS install! ) and it's not too hard once you can see what is confusing it.
However, once done, NEVER, ever re-enter Displays unless you are sure the bug is fixed, as you'll have a high probability of a incorrect monitors.xml file.