Does it work, if the Mac is shut down?
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What to do if the wrong device responds to ”Hey Siri”
- Make sure that each device has Bluetooth turned on. If Bluetooth is turned off or a device isn’t in Bluetooth range of the other devices, multiple devices might respond to your request.
- Make sure that each device is using the latest Apple software. If some are using older software, multiple devices might respond to ”Hey Siri.”
- On each device that you want to use with ”Hey Siri,” make sure that ”Hey Siri” is turned on in Siri settings.
- If you have an iPhone or iPad, you can place it face down so that it doesn't respond to ”Hey Siri.”
- If you have a HomePod, you can say ”Hey Siri, turn off Hey Siri,” or use the Home app to turn off Listen for "Hey Siri.” To turn it back on, touch and hold the top of HomePod, then say ”Turn on Hey Siri.”
- If you have a Mac that supports ”Hey Siri,” you can close its lid so that it doesn't respond to ”Hey Siri.” And if ”Allow Siri when locked” is turned off in Siri preferences, it also doesn't respond when the screen is locked.
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copied from: How 'Hey Siri' works with multiple devices - Apple Support