No email get after buying the downloadable product

Hi there,

That’s indeed how the WooCommerce plugin works provided that the payment notification from your payment gateway reaches your website successfully AND the order status is changed to “completed” automatically.

If you’d like to send additional follow-up emails, you could look into using https://woocommerce.com/products/follow-up-emails/ or https://woocommerce.com/products/automatewoo/