Thank you for your answer. But this does not quite solve the problem. The incoming email does not bounce now and is put into the mailbox of the specified local system user (/var/spool/mail/username).
This is not what I want. I have created virtual Mailboxes in ISPConfig and I want those emails to go there.
With Thunderbird, for instance, I can only log in (via IMAP) with the username and password of the virtual Mailboxes created in ISPConfig, but not with the credentials of local users. So this works fine for outgoing emails, and I can also send emails from those Mailboxes.
But how can I tell Postfix / SMTP not to handle incoming emails on their own but to ask ISPConfig what to do?