I believe the option you have selected deals with the download and storage of IMAP account messages for offline use. It is not intended to effect which messages are displayed in the Inbox or other IMAP folder for reading and interaction.

so the next question is: Have you got the option to synchronize all folders checked or have you selected specific folders for synchronization and other folders are just subscribed?

• https://support.mozilla.org/en-US/kb/imap-synchronization#w_configuring-synchronization-and-disk-space-usage

What's the difference between subscribe and synchronize? The page at that link doesn't contain the word subscribe.

Thunderbird defaults to only showing subscribed folders. That's a way to manage the clutter when you have a lot of remote folders and you don't want to see all of them in the folder pane. You subscribe a folder by right-clicking on the remote Inbox, selecting "Subscribe", expanding the Inbox tree in the window, and subscribing whatever folders you want. You can configure it to show all folders by unchecking the checkmark at "Tools -> Account Settings ->Server Settings -> Advanced -> IMAP -> Show only subscribed folders".

Thanks.

In case anyone at Mozilla reads this:

It is staggeringly confusing to have these various folder functions that are completely connected at every level located in two completely different, mutually inaccessible locations in the settings. I am a 'power user' who has taught myself GIS and advanced statistics software (SAS) and can say the folder management is far more confusing than it needs to be.

I've been casually looking around the settings for months trying to figure this out, assuming - incorrectly - that something so basic will be self-explanatory, i.e. under "Server" or "Synchronization" settings. I didn't make a focused effort because it was inconceivable it wouldn't be somewhere in there. People shouldn't have to dig around in forums and post questions about this.