How To Hook To Commerce Add To Cart Button After Add?
You've got a rules event that fires when a product is added to the cart, which is called after the price calculation one, check commerce_cart_product_add function.

It uses rules_invoke_all, which means that you can either run actions on this event or invoke the hook directly, hook_commerce_cart_product_add normally.

// Invoke the product add event with the newly saved or updated line item.
rules_invoke_all('commerce_cart_product_add', $order, $product, $quantity, $line_item);