First when you register your custom taxonomy use the capabilities argument and define your custom capabilities:
'capabilities' => array(
'manage_terms' => 'manage_cities',
'edit_terms' => 'edit_cities',
'delete_terms' => 'delete_cities',
'assign_terms' => 'assign_cities'
),
and only give your users the assign_terms capability this way they wont be able to create new terms, only YOU.
Then use the nice solution you linked in the comment ,
change the $taxonomies_to_sync array according to your taxonomy, and you should be fine.