How can I stop home app from sending notification to everyone when an action is taken?

You can turn off the notifications for this particular accessory:

• Open the Home app.
• Tap or click an accessory, then tap or click the Settings button .
• Select Status and Notifications.

• Turn Activity Notifications off.

I can’t think of any other setting that would disable the notification to the other members of the household. I guess they would have to turn it off on each of their individual devices if they do not wish to receive it.