Cashu does not put satoshis INTO bearer ecash tokens. It issues an independent token which on its own is incompatible with every other cashu mint doing the same.

A mint itself takes possession of the sats, and offers a service to

- give you tokens for sats

- swap tokens for fresh tokens

- accept requests to pay bolt11 lightning invoices denominated in satoshis and provides an offer exchange rate

- may fullfill payment of aforementioned invoices through bridging to lightning network.

When you send satoshis to a cashu mint, you are effectively selling your sats for tokens under the hope that you can later get some of that value back.