Message filters do not run when new mail arrives even though this option is checked
When new mail arrives in an IMAP mailbox, the filters only work on unread mail, not new mail that has been read on another device (but which is still newly downloaded to Thunderbird).
When a filter delivers new mail (read or unread) to a local folder, the filters for that folder are not run - they have to be run manually.
Alla svar (1)
Filters are auto run on new unread mail that is downloaded to the Inbox for that account.
As IMAP mail accounts see a remote view of the server, the folders are in effect one and the same regardless of how you view them. As you had previously accessed the server and read the email, it will no longer be new unread mail as that setting will have been set on the server.
As a test, I suggest you mark the previously read emails as 'unread' at the time of reading whether this is via a phone or webmail and see if this triggers the filter when you view emails via Thunderbird.