When invoices are on Auto-Publish and have been published, you'll be alerted to that in AutoEntry in two ways. 

Firstly, the standard publish button is replaced by a green Lightning bolt in the Inbox/Archive folder:

Secondly, a notification banner will appear at the top of the page in the inbox to let you know AutoEntry has auto-published 'x' amount of invoices. 

The settings for Auto Publish can be set for each supplier under Supplier Settings

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