wpcargo_after_save_shipment hook is used in saving additional shipment data.

//Save date updated
function date_updated_metakey_callback($shipment_id, $data){
    if( isset($data['date']) ){
        update_post_meta( $shipment_id, '_date_updated', $data['date'] );
    }
}
add_action('wpcargo_after_save_shipment', 'date_updated_metakey_callback', 10, 2);