We use a system called Brightpearl which is integrated with Shopify via an App.
When we pass an amazon Tracking number through to Shopify we seem to get an incorrect Carrier assigned to the tracking number. This in turn causes issues for our customers as they cannot track their order (i.e. StarTrack).
After a bit of investigating I've found out that the problem with the Shopify tracking link taking us to the wrong tracking site can be caused by Shopify receiving the wrong shipping method. When this happens, they look at the number of digits in the tracking reference and any prefixes in this reference to try and guess the shipping method, this is often guessed incorrectly by the system though, resulting in the tracking links not taking you to the right website.
From what I can see in the logs and also on the GONs in Brightpearl, we have sent the correct shipping methods to Shopify, and the Shipping method mapping in our Shopify account is set up correctly.
For all other carriers, the Carrier method is mapped correctly on Shopify.