No, funds never leave your PC. Coin Pairs do not yet cover FIAT, it is from one crypto coin to other. At one important moment , once full match and consensus is reached, by one atomic swap your coins (those which you sell) leaves your wallet, and the new , other coins, which you buy - apears in your other coin wallet in your PC. And there is no need to trust any third party, like the centralized exchange. Plus - there is no need for KYC, registration, identification of yourself, and other bad things like that.
No, funds never leave your PC. Coin Pairs do not yet cover FIAT, it is from one crypto coin to other. At one important moment , once full match and consensus is reached, by one atomic swap your coins (those which you sell) leaves your wallet, and the new , other coins, which you buy - apears in your other coin wallet in your PC. And there is no need to trust any third party, like the centralized exchange. Plus - there is no need for KYC, registration, identification of yourself, and other bad things like that.