Ok now - only one simple question - am i the ONLY one with this problem here? i cant believe it sorry.
No, you're not. It's the same problem if you would use windows live mail or Outlook.
But please follow one of the suggestions to solve your problem.
Kess also wrote "..and as I can see you still continue to use web4you-gmbh.ch as the CN for your certificate", if this is true and in your postfix conf I can see "myhostname = web4you-gmbh.ch" it can't work with mail.web4you-gmbh.ch or smtp.web4you-gmbh.ch for example. You can't use subdomains if your cert only knows web4you-gmbh.ch.
Do the following (for testing):
change your hostname to mail.web4you-gmbh.ch, create a cert for mail.web4you-gmbh.ch and change the hostname in your postfix conf to mail.web4you-gmbh.ch
All your customers only need mail.web4you-gmbh.ch for "Posteingangsserver" and "Postausgangsserver". This is how it works for me.
Best regards