Solution:
That is very simeple as you will see… It can be done just adding 'update_totals_on_change'
to billing email and phone fields wrapper class, this way:
add_filter( 'woocommerce_checkout_fields' , 'trigger_update_checkout_on_change' );
function trigger_update_checkout_on_change( $fields ) {
$fields['billing']['billing_phone']['class'][] = 'update_totals_on_change';
$fields['billing']['billing_email']['class'][] = 'update_totals_on_change';
return $fields;
}
Code goes in functions.php file of your active child theme (or active theme). Tested and works.
But sometimes depending on your code, it will be not enough.