There are a couple of gotchas to watch out for when configuring Horde IMP to work with Cyrus IMAP.
When using Cyrus configured for virtual hosts, and the standard IMP config, folder handling appears to be broken.
To make virtual hosts work with Cyrus you had to put unixhierarchysep: yes in your imapd.conf - you already knew that part, right? ;) -> this is not correct, Cyrus works at my server with multiple virtual hosts without reconfiguring the unixhierarchysep.
Given this, a change is required in the imp/config/servers.php file: edit that file and make sure you use a slash (/) after the 'INBOX' in namespace instead of the usual dot (.):
... 'namespace' => 'INBOX/', ...
This is no longer required with IMP 4.1 or later, because namespaces are detected automatically in newer versions.