Whoever is running the mint. My basic understanding is that the mint is effectively running a custodial lightning node with a cashu mint on top. The bitcoin funds sit in a lightning wallet and cashu tokens are generated and regenerated as they are used or redeemed. If a token is redeemed at a second mint, the second mint effectively requests a lightning payment from the first to redeem the tokens. 

It’s like a lightning wallet that functions as a bank issuing redeemable, private IOUs