How can I stop my iPhone messages from sharing to my iPad

If you own and use both devices, then you cannot. by design messages are synced.

You can turn off the option to share SMS messages to the iPad by going to Settings ➜ Messages ➜ Text Message Forwarding on your iPhone, however iMessages (blue bubbles) will continue to arrive at the iPad, unless you turn off Messages there entirely on it.

If someone else is going to be using this iPad, then it's best they have their own Apple ID as suggested by the support document you posted from. Make sure it's signed in to all services on the iPad including Messages.