At least that is their claim. If you look into CDC's own documents you'll find that their tests do not identify the variants. In fact, they often do not differentiate between COVID and INFLUENZA. The CDC has indicated to detect "Delta" and other variants you need to specially send the sample to a specific lab and they are only doing that on an occasional basis.

Yet since they still haven't actually isolated COVID how do they know?

Answer: They don't.