If your customers check out using the dynamic checkout buttons on the cart page, then the bundle discounts won't get applied. However, if they first go to the Shopify Checkout and then click on one of these buttons, then the discounts will get applied.
This is why we have an option which allows you to hide these dynamic checkout buttons on the cart page when the customer qualifies for the bundle discounts. And as mentioned, the customer can then still use these payment buttons in the Shopify Checkout.
You can turn on this option in General settings -> Advanced (at the bottom of the page).