If you look at Allan's page, the basic "throat controlled relay" is inside the Tortoise when you are using 2-7 contacts. As you set the route through the throat (using contacts 1 and 8), the other contacts change accordingly, allowing the polarity to be swapped (and some people will call this "extended power routing", by the way). Allan does show a color version of the tortoise contacts below #4 of the "Reversing a Balloon Track with a Tortoise".
If you don't use the Tortoise contacts, he shows you can use an external separate relay in the first diagram under #1. The relay is above the block labelled "Tortoise".
The DPDT switch on the left side of that same diagram is used to control both the route through the turnout and the loop polarity.
So, the "throat controlled relay" is just the relay part, not the DPDT switch or the combination of the DPDT switch and the relay.
Hope this helps!
The action of pubining the selection of the turnout setting (contacts 1 and 8) and an additional relay outside of the tortoise onto a DPDT switch used to control both the Tortoise and the track polarity.