This issue applies to address books created in Outlook, not address books created in Zimbra Web Access.

Pre-existing contacts in multiple address books (address books other than the default) will not synchronize to the device.  New contacts added to the address book on the Zimbra server will synchronize to the device, however, initial contact loads or contact reloads will not synchronize the pre-existing contacts.

This is not the case with the default address book.