Our app uses Shopify's draft orders API to create orders with discounts. Draft orders are the cleanest way to offer discounts which is why we use them. How it normally works is:
1. The customer clicks the checkout button on the cart page.
2. Our app creates a discounted draft order and then immediately takes the customer to checkout with the discounted draft order.
3. Once the customer completes payment, the draft order is converted into a regular order in Shopify, and it's at this time the order will likely hit your warehouse.
Because it's still a draft order until payment is made, it will not hit your warehouse until the customer completes payment.
Shopify has details on draft orders here:
If this is a showstopper for you, I recommend trying a discount app that does not use draft orders. Some discount apps use normal orders (not draft orders) with different methods of giving discounts, including:
1. Discount codes (total Bulk discount is added as a discount code to the order)
2. Duplicate hidden variants (duplicate hidden variants, each corresponding to a different wholesale price)
As you can imagine, these options both have serious drawbacks as well.