This website uses an open source Bitcoin Cash library called Datacash to construct and broadcast OP_RETURN Bitcoin Cash Transactions.
1. All the signing takes place 100% on the client side so your private key is safe. (Check out the source code to make sure)
2. After the signed transaction is constructed, you can broadcast it to Bitcoin Cash network by pressing the "Send" button. This will broadcast the signed transaction through a public JSON-RPC endpoint.