The updates are supposed to be automatic. I would look on the carousel to see if the books have been added at the front of the queue, also if they show up first when sorting "By Recent". If either of these are true, then the book has been updated. If not, it might still have been updated because the Fire's new stuff management is flaky.
If you are unsure, try deleting the ebook from the Fire and then restoring it from the Cloud.
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