My opinion (and sorry, I know you asked Peter...) is that YES, they should use mail.prodesigner.ch for both SMTP and IMAP/POP3, and I can assure you that it works (I'm using the same kind of configuration, for several domains...)
Only thing I can imagine for why it didn't worked for you, is because your cert wasn't issued for mail.prodesigner.ch but only for prodesigner.ch, www.prodesigner.ch and eventually webmail.prodesigner.ch. If this is the case, just add mail.prodesigner.ch as an alias of prodesigner.ch and request a new cert which include mail.prodesigner.ch too
Edit: when I'm talking about "alias" I'm not meaning a simple CNAME but a domain alias, at Plesk level...
Hi there - Thanks for the great advice on this post. I have an issue which I think is the sam / VERY similar.
I am running a clients domain on my plesk server, when trying to use ms outlook, they are presented with errors referring to an expired plesk cert and NOT the Lets Encrypt cert that is active on their domain. So following your advice I realise that when creating a domain alias I am presented with the option of specifying www.xxxxxxx.com by plesk (pls see attached image). Do I just create an alias www.mail.xxxxxxx.com ?
Should I keep all of the other checkbox option ticked too ?
Thanks in advance all.