Hello, hellwoodfire.
Most important question first:
What exactly is it that makes you assume that Update Manager upgraded your Cinnamon, but not xfce, KDE and Mate, when upgrading from Mint 17.2 to Mint 17.3?
Preface:
1.5 years ago I installed Linux Mint 17 Qiana Cinnamon on one of my machines. Later on I added the xfce desktop to it. Not by using the Xubuntu Developers PPA like you, but by following this instruction:
xfce instead of mate (Do not let yourself be confused by the title. The link leads to an instruction on how to add the Mint xfce desktop to the (primary) Cinnamon desktop.)
At that point in time I was running Linux Mint 17 Qiana Cinnamon + xfce.
When Mint 17.1 Rebecca Cinnamon and Mint 17.1 Rebecca xfce had both been released and
the upgrade from Mint 17 to Mint 17.1 through Update Manager enabled for both, I simply upgraded Mint 17.0 Cinnamon + xfce to Mint 17.1 Cinnamon + xfce through the Linux Mint Update Manager.
Upgraded level 1, 2 and 3 software packages. Worked like a charm.
Since then I am running Linux Mint 17.1 Rebecca Cinnamon + xfce.
The system works like a charm. Switching between Cinnamon and xfce in the login screen works like a charm. Cinnamon and xfce do not interfere with each other. (Took some extra steps not mentioned in the linked thread above, to make sure they do not do so.)
Annotation:
I have never considered adding two more DE's to the Linux Mint 17.1 Cinnamon + xfce system, KDE and Mate. The main reason for not doing so is that this will envitably lead to some level of clutter, because each DE will bring along a list of system applications, which each of the 3 other DE's will bring along, too.
But basically, having 4 DE's on Linux Mint 17.2 should work / should have worked.
About upgrading Linux Mint 17.2 Cinnamon + xfce + KDE + Mate to Mint 17.3 in one go:
Basically even this should have worked / should work, provided you have not done so before Mint 17.3 was available for all 4 desktop environments.
The announcement that Update Manager permitted upgrading from Mint 17.2 to Mint 17.3 for all 4 DE's was published January 6th, 2016:
Upgrade path to 17.3 now open for all editions
Unless you have tried to upgrade your Mint 17.2 4 DE's to Mint 17.3 before January 6th, 2016, Update Manager should have been able to upgrade your whole system in one go.
Potential Pitfalls:
xfce:
You have not added the Linux Mint xfce DE to your Mint 17.2, but xfce from the Xubuntu Developers. This may have brought about some differences which may have prevented the Update Manager from correctly upgrading your xfce when it upgraded Mint 17.2 including the Cinnamon DE to Mint 17.3.
Mate / KDE:
You have not explained how exactly you have added Mate and KDE to your system. In case you have added them in a non-standard way like your xfce, then this may have "confused" Update Manager.
Most important question repeated:
What exactly is it that makes you assume that Update Manager upgraded your Cinnamon, but not xfce, KDE and Mate, when upgrading from Mint 17.2 to Mint 17.3?
Note:
"inxi -S" will always just display the currently loaded desktop environment and its version, never any additional DE.
So in order to find out which
- Cinnamon you are using, you have to login to Cinnamon and run "inxi -S".
- Mate you are using, you have to login to Mate and run "inxi -S".
- xfce you are using, you have to login to xfce and run "inxi -S".
- KDE you are using, you have to login to KDE and run "inxi -S".
Cheers,
Karl
(the favorite of each member of my familly).
Can I upgrade everything at once ? 
