Apple TV subscription

You need to redeem the offer yourself, it’s not done automatically.

Offer must be claimed within 90 days from when you activated the new device 

Open the Apple TV app. Make sure your device is running the latest version of iOS, iPadOS, tvOS, or macOS.

The offer should be presented immediately after launching the app. If not, go to the Apple TV+ channel page where you’ll see the offer.

Tap Enjoy 1 Year Free.

Apple TV + Offer

https://support.apple.com/en-us/HT210573

The offer will be for the first qualifying purchase. You would need to setup that device and claim the offer. Once the offer is claimed it will be available to all devices signed in with that Apple ID.