You can easily see which publishers have auto-approved your requests on your Dashboard, near the bottom of the page. Click on the publisher's name to browse their available digital review copies and audiobooks.
You can also view a full of books from all publishers who have auto-approved your requests in Find Titles. Under Browse, click on the Auto-Approvals link (you must be signed in to view this):
Remember, when you are auto-approved by a publisher, you receive an email notification. You can instantly access any of the publisher's available books by clicking “Request.” Your request will be automatically approved, and the books will be accessible in your account.