Being auto-approved by a publisher means you are now instantly approved for any of that publisher (or imprint's) books on NetGalley. Press the "Read It!" button and you will be approved right away.
Take advantage of your auto-approval! Be sure to use the Auto-Approvals section under Browse in Find Titles and on your Dashboard and check back for new books from that particular publisher on a regular basis, since you'll be able to access those books as soon as you press the "Read It!" button.