The multisignature in the tutorial is 2-of-2, meaning that two different signatures are required from two different private keys. There is one key in each MultiChain node, each on a different server.
So you can use action:sign without supplying a private key, because the private key for signing the multisignature on behalf of one address is already in that node's wallet. Then the second server needs to sign the same transaction, after the first has signed it, and the transaction is passed from one to another as a hex blob.