First, I did add a custom target by running firebase target:apply demo my-project. However, when running firebase emulators:start --only hosting:demo I receive the following error message:

Error: hosting:demo is not a valid emulator name, valid options are: ["auth","functions","firestore","database","hosting","pubsub"]

As per documentation (https://firebase.google.com/docs/hosting/multisites?authuser=0#cli-commands-with-deploy-targets) firebase emulators:start --only hosting:TARGET_NAME should emulate the Hosting content and configuration of the specified Hosting site at a locally hosted URL.