Custom Hook save_post

add_action('save_post', 'xx_assign_parent_terms');
add_action('save_post_product', 'xx_assign_parent_terms');
add_action('woocommerce_update_product', 'xx_assign_parent_terms');

function xx_assign_parent_terms($post_id){

global $post;

if(isset($post) && $post->post_type != 'product')
    return $post_id;

// get all assigned terms   
$terms = wp_get_post_terms($post_id, 'product_cat' );
foreach($terms as $term){
    while($term->parent != 0 && !has_term( $term->parent, 'product_cat', $post )){
        // move upward until we get to 0 level terms
        wp_set_object_terms($post_id, array($term->parent), 'product_cat', true);
        $term = get_term($term->parent, 'product_cat');
    }
  }
}

I am using this code to add parent terms when a product category is updated. It works on default WP product create/edit pages. It also works on BEAR when category of a SINGLE product is modified.
It does NOT work when category is modified for multiple products.

Is there a different hook I should be using?