Master Site for specific taxonomy in MultiSite

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.