Once the customers access your online store and navigate to the product’s detail page, they will see the volume discount tables as configured from the app backend.  Here, the customers will see discounts on minimum product purchases.
If you have configured the cart custom message by inserting the liquid variables, the customers will see the message on the cart that they need to buy other products to be eligible for the discounts. 
Once they are eligible for the discounts, they would check out and navigate to the checkout page. Here, the customers will see the applied discounts on the checkout details.