According to the included /usr/share/offlineimap/offlineimap.conf example configuration file, you have to set idlefolders to a list of folders to monitor.
########## Advanced settings # ... # In between synchronisations, OfflineIMAP can monitor mailboxes for new # messages using the IDLE command. If you want to enable this, specify here # the folders you wish to monitor. Note that the IMAP protocol requires a # separate connection for each folder monitored in this way, so setting # this option will force settings for: # maxconnections - to be at least the number of folders you give # holdconnectionopen - to be true # keepalive - to be 29 minutes unless you specify otherwise # # This feature isn't complete and may well have problems. See the manual # for more details. # # This option should return a Python list. For example # # idlefolders = ['INBOX', 'INBOX.Alerts'] #