To manually update an OAB, see Use the Exchange Management Shell to update offline address books.
However, synchronization of the shadow copy between organization mailboxes is performed on-demand.
Here's how it works: In Exchange 2010, moving OAB generation to another server required you to specify a different generation server in the properties of the OAB.
OABs in Exchange 2016 are improved over OABs in Exchange 2010.
These changes were introduced in Exchange 2013: OAB generation is controlled by the mailbox assistant named OABGenerator Assistant that runs under the Microsoft Exchange Mailbox Assistants service.