From the article:
To choose when your device receives Intercom notifications, select which members of your Home have access to Intercom, and choose which HomePod speakers use Intercom:
I suspect Apple's intent is that all devices in a physical home are are added to the same Home, and thus attached to one Apple ID. The other users need to be joined to the Home so they can activate Intercom. See Share control of your home - Apple Support. Alternatively you each try inviting the others to join the Homes that you have created, but I can see that it could get complicated.
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