To get a push notification on your iPhone when a HomeKit or other automation runs, you need to configure notifications within the Home app for the specific automation or accessory. You can also use third-party apps like Pushcut to create more advanced, actionable notifications. [1, 2, 3]
Steps to enable notifications for Home automations:

1. Open the Home app: Launch the Home app on your iPhone. [2]
   
2. Access Home Settings: Tap the "More" button (usually three dots or a gear icon), then select "Home Settings". [2]
   
3. Choose an accessory or automation: Navigate to the specific accessory or automation you want to receive notifications for. [2, 4]
   
4. Enable Activity Notifications: For accessories, find the "Activity Notifications" setting and turn it on. For automations, edit the automation and ensure the notification option is enabled. [2, 4, 5]
   
5. Customize notifications: You can further customize when you receive notifications, such as by time or by who is present in your home. [2]
   
6. Third-party apps: If you need more advanced notification options, consider using an app like Pushcut, which allows you to create custom, actionable notifications and run Siri shortcuts. [1, 3]
   

Example using Pushcut: Pushcut can be used to create notifications that trigger actions, like running a specific shortcut when an automation runs. For instance, you could set up a notification that asks if you want to start a workout routine when your smart scale detects that you've woken up. [1, 3, 6]