Maybe is with taproot channels then, not sure about the technicalities. Considering USD are just zeros in a screen, they keep the record of X$ received and trigger a send BTC to the user@cashup.me lighting address, that's basically a subaccount on Cashup LN node. However consider this just a logical speculation, there are probably other ways to do it.

The sats move out of Cashup LN node only when BTC are sent to an external address, lightning or onchain.

Would be interesting if you could run some test, try for example sending a small amount, like 1sat to your didiplaywell@stacker.news (or any other) lightning address and see what happen. Try also the other way around.