Go to Shopify Admin > Settings > Shipping > General Profile > Manage Rates
You should see the app's logo underneath your zone, like in the screenshot below.
If you don't see the app connected as a calculated rate under each zone you want to the app to show rates for, you must add the app to your zone.
Add the app to your zone
Under the zone, click the Add rate button.
Then select Use carrier or app to calculate rates
Choose Advanced Shipping Rules from the dropdown menu.
Check all the services that show up if there are any
Check Automatically show new shipping services to customer when they become available
Then click Done
Then Save the zone.
Then open the app, and go to the Sync tab, and click Sync Shipping Zones