You could make use of WordPress’ get_term_children() function on the save_post hook. A nice thing about this is that get_term_children() is recursive and collapses to a single dimensional array, so if you were to ever add smaller subdivisions as a third, fourth, fifth level, etc – you will automatically grab all hierarchical children with it.

You don’t specifically mention what taxonomy you’re using, but you say Category in your post. I’ve used the term/taxonomy functions instead of the category functions because it lets you adapt easier to custom terms/taxonomies later a bit easier. In this scenario, ideally you’d have a custom taxonomy like “Location” and the terms “Africa, Asia, etc.” would be under that.

This is a bit verbose and is a bit on the “verbose” side to be safe, but it should work to get you started at least:

add_action( 'save_post', 'so_60079535_put_post_in_child_terms', 11 );
function so_60079535_put_post_in_child_terms( $post_id ){
    // Get the terms for this post
    $taxonomy = 'category';
    $terms    = wp_get_object_terms( $post_id, $taxonomy );

    // If the tax doens't exist, or something fails, abort
    if( is_wp_error($terms) )
        return;

    // If there are none in this tax, abort
    if( empty($terms) )
        return;

    // Loop through terms to find any children, recursively
    foreach( $terms as $term ){
        $child_terms = get_term_children( $term->term_id, $taxonomy );

        //if tax doesn't exist or error, skip this term
        if( is_wp_error($child_terms) )
            continue;

        // If no children, skip this term
        if( empty($child_terms) )
            continue;

        // APPEND these child terms to the parent post object
        wp_set_object_terms( $post_id, $child_terms, $taxonomy, true );
    }
}