Find out which discount is applying
At checkout, the discounted shipping rate shows the name of the discount underneath it:
For automatic discounts made with this app, that's the discount's Title.
For code discounts, it's the code.
If the name isn't the discount you're looking at in the app, a different discount is applying. It might be an older duplicate, a Shopify discount or another app's. Find it in Shopify admin → Discounts and deactivate it if it shouldn't be there.
Common causes
Two discounts qualify. Only one shipping discount applies to a rate, and Shopify picks the one that saves the customer the most. A broader discount can win over the one you meant.
A threshold is being met that shouldn't be.
Cart subtotal ignores discount codes. Use Cart total if the threshold should be after discounts.
Cost of items from collection (subtotal) is also before discounts. Use the (total) version.
The amount looks wrong.
Fixed Amount Off can't take a rate below $0. A $25 credit on a $19 rate makes it free, not -$6.
Fixed Price leaves cheaper rates alone.
Other currencies convert at Shopify's exchange rate, so the amount differs slightly from your store currency. See Selling in multiple currencies.
The discount is on the wrong rate.
Cheapest shipping rate picks by price, from shipping rates only (not local delivery).
Choose specific rates with a typed (wildcard) name matches any rate containing that text. "Post" matches "Express Post" and "Parcel Post".