The way it works right now is that you would upload one of those old speeches or radio shows to the API, and then you'd get back a transcript that includes all the "terms of art" you customized the API to be able to recognize. Right now there's no feedback loop for you to tell the API where it was wrong, but that's something we have in mind to build! We do run QA across our entire API usage though, and from that are able to improve recognition accuracy over time. We also release updates to the models that power the API every few weeks which improves recognition accuracy too.
And then we do provide confidence scores, so we can at least give you some indication when we're not confident in the automatic transcript we're returning to you.
If you want to try out the API, you can email beta@assemblyai.com and I will look for your mail!