Hi Danny,
Sorry for the late reply.
If you would add it to the cart page, it would depend on the selected “Position”. For example, if you select the “Cart: After cart totals” position, then the info will be updated. On the other hand – if you select “Cart: After cart” position – info will not be updated and your customer will have to refresh the cart page manually to see the updated info. In other words – the position must be inside that part of the cart page that is being refreshed after cart content changes.
Now if you’ve added it manually to the Shop page – unfortunately, the only solution I can think of – is to disable “Enable AJAX add to cart buttons on archives” checkbox option in “WooCommerce > Settings > Products > General” – this way the page will be automatically reloaded once user adds a new product to the cart.
Hope that helps.