It sorted itself out. Actually I still don't know what went wrong, but I reinstalled ISPconfig again using the same settings except that I chose not to encrypt the keys from the beginning and I also chose http. It all just suddenly worked.
Now there is another more specific question I have. In roundcube there is normally no way for email users to change their passwords. If you want to do that you can enable mail login for the site and then reach it on http://mywebsite.com:81/mailuser/
Since this is a bit awkward and definitely not what people are used to doing it is better to have the password change from the webmail client (roundcube in my case).
In DirectAdmin this can be done by adding a frame to roundcube with some commands from DirectAdmin (http://youserver:2222/CMD_CHANGE_EMAIL_PASSWORD
). (see http://www.directadmin.com/forum/showthread.php?t=21684
for details ).
Is there a similar function in ISPconfig or does someone know of another way of doing this?