First validate if the shipping prices are indeed wrong.
Go to Google Merchant Center > Products > All Products > select your product > Scroll down till you see final attributes.
Also check what prices are created in your shipping app. If the shipping app is accurately setting your prices, then the issue is the communication between your shipping app and the free google shopping app.
In this case, I recommend you contact the shipping app support team. If they can’t resolve it, contact shopify support team as they own the app you are using.
If all fails, then you need to setup the shipping settings manually using the guide here: https://support.google.com/merchants/answer/6069284?hl=en