This feature has been broken for over 2 months. Shipments shipped via Amazon MCF and connected via the Shipstation integration aren't carrying the carrier back in the payload.
Shopify is smart enough to classify the USPS shipping numbers as USPS and the UPS tracking numbers as USPS, however shipments shipped with Amazon Logistics show up as blank.
If the Shipstation/Amazon MCF integration worked correctly and Shipstation actually pulled in the carrier from Amazon MCF, this wouldn't be an issue. Kind of unbelievable this has been broken this long and no one at Shipstation will fix the integration.