Hello,
Variable products do not use Ajax Add to cart by default that’s why you don’t see that effect but only default WooCommerce notification after page reloading that product is added to cart. You may try third-party plugins to add the Ajax add to cart for the variable products https://wordpress.org/plugins/woocommerce-ajax-add-to-cart-for-variable-products/ or https://wordpress.org/plugins/woo-ajax-add-to-cart/ but I’m not 100% sure that it will call our mini-cart after adding to cart. Anyway, you may try.
Regards