When checking for new messages in IMAP accounts, Postbox only checks each account's Inbox by default. However, it's possible to include other IMAP folders easily. Here's how:
Find the folder in the Folders Pane that you'd like to check for new messages. Right-click (or control-click on Mac) on the folder, and select Properties... Then, in the subsequent window, check the option to "Check this folder for new messages".
Repeat this process for each folder that you'd like Postbox to include.