How to render node content according to site theme after hook_node_insert/update?
So first as the hook_node_update doc says: 


  Note that when this hook is invoked, the changes have not yet been
  written to the database, because a database transaction is still in
  progress. The transaction is not finalized until the save operation is
  entirely completed and node_save() goes out of scope. You should not
  rely on data in the database at this time as it is not updated yet.
  You should also note that any write/update database queries executed
  from this hook are also not committed immediately. Check node_save()
  and db_transaction() for more info.


Solutions:

There's a module for that: hook_post_action

There's also a short article about drupal_register_shutdown_function