Virtualmin doesn’t need to know much about the IMAP server running on your machine – I wouldn’t be too worried about that aspect.
What I would do is:
Figure out where on the filesystem Postfix/procmail are delivering emails.
Setup Cyrus to store/retrieve emails at that same location.
Verify that Usermin is either reading the emails from the correct location on disk, or maybe even set it up to grab emails via the IMAP server rather than looking at the disk directly.
Okay, I’ll digg into Cyrus first- maybe it’s just an configuration option somewhere.
Yeah, Cyrus does store mail elsewhere: /var/spool/imap/domain contains my domains. And it doesn’t seem to use maildir either- it makes folders with thingy.cyrus in it. So reconfiguring Cyrus is essential.
All right, I’ve solved it by using Dovecot and waved bye-bye to Cyrus. Now everything works.
Hehehe…Funny how that works. Probably wise. 
Dovecot, in my experience, is dramatically easier to use than any other POP/IMAP servers I’ve met.
Well, it looks nice all right. Can you modify my first post and add ‘solved’ in the header?
No need to clutter up the title. Things cycle pretty quickly on the forums, so it’ll be completely forgotten in a week.