Have you explicitly copied books to the Mac?
The authorization system allows books to be read across multiple devices authorized to the same ID, but does not automatically synchronize/copy the books.
On authorization: I can't verify what the Mac versions does, but v1.7.2 on a PC shows just the email address as authorization,
but V2.0 shows the email address and also the internal id (urn:uuid:xxxxxx) where xxx is a string of numbers, hyphens and letters a to f.