No thats not possible, due to the way how Exchange 2013 and 2016 works and that people want to achieve full segregation this is necessary.

I run the command

Get-Mailbox myusernameinproblem | select name, DefaultPublicFolderMailbox

and i can see the user having the problem was indeed bound to the PF he was supposed to be

yet he got the prompt for ANOTHER PF.

Can that be a bug in SolidCP?

Please make sure you do this for all (by executing the script or manually applying it to all), it's the known fix for this issue.

SolidCP has nothing to do with this, it's just Exchange 2013 / 2016.

SolidCP does apply all the correct segregations, however all the existing / previously created mailboxes are left untouched and will not follow that logic (as SolidCP only applies it to mailboxes it's creating).

I run the script, got errors etc

The problem seems to be that although users have the proper PF bound they get a message for ANOTHER domain.

(Of course they can press "do not ask me again" and proceed, but this is not very professional...)

Well as i mentioned for ou's that already got it set it will error and continue (expected behaviour). The script should complete in full tho.

The box you mention once done for all OU's should then be gone once your address lists have been updated. there's really nothing more to it then that 🙂