Unfortunately, the app is completely blind to discount codes and line item discounts. 

When Shopify sends information to the app to calculate rates with, it doesn't include any line item discounts or discount codes. Only the original prices of products in the order are provided.

So, free shipping rules, price based rules, and priced based rates will always be based off the non-discounted product prices and cart totals. You will have to take this into account when running discount code promotions, and setting your free shipping thresholds.

We recognize that this is a very frustrating limitation, we are frustrated as well that we can't offer this as an option. This is a current limitation for all 3rd party shipping apps, not one unique to Advanced Shipping Rules.