Yes — the app does support Shopify Automatic Discounts.
Turn on this feature to apply applicable discounts automatically for customers during checkout.
NOTE: If the new draft order flow is not enabled within the App setting, the Automatic discount only applies on the Product base price. In order to apply discount on total amount of order that inlcludes add on charges, please enable below from Settings>>General Settings>>Use new draft order flow
Outcome: 
