The add-in sets the flags but it's Outlook which acts on them, so it shouldn't be necessary for the recipient to have the add-in - but things are obviously not working here...
The add-in does also show the current state of the flags on received message windows (and lets the recipient re-enable the associated behaviours!) so I guess that installing it on the others' machines would let you see if the flags are being dropped en route
vs Outlook ignoring the settings (neither of which should be happening, of course).
I admit I know nothing about how Exchange is configured - maybe there's some setup option that ignores these flags? (Just speculation.)
If you have the time, maybe take a look at
https://blogs.msdn.microsoft.com/gsmyth/2011/08/06/outlook-object-model/ and see if the PowerShell script for displaying 'actions' works on the sending and receiving machines: might give some more clues about where the info is getting lost - though I can't
think of a way to compensate at the moment, wherever things are going wrong.