Hi,
Please make sure that the "HikaShop cart notification" plugin is activated in the Joomla plugins manager.
Also, it seems that the file "cart" of the view "product" was customized with code from an old version of HikaShop. Because of that, the cart module isn't refreshed dynamically after the add to cart.
I would recommend renaming the file templates/YOUR_TEMPLATE/html/com_hikashop/product/cart.php in order to deactivate that customization and add it back to the new version of that view file via the menu Display>Views of HikaShop.