To redeem the T-Mobile offer, you have to follow the procedure as this partnering company describes: Select that you want the offer, to link it to your T-Mobile account, and then activate with Apple: link your Apple ID account to the Apple TV+ offer.
Note that the Apple ID account also has to have a linked pre-authorized payment method. This is required for all subscriptions through Apple. You won’t be charged for it as long as the T-Mobile perk is valid, ᴀɴᴅ for as long as you keep it limited to Apple TV+. Buy or rent titles or other subscriptions are not part of the Apple TV+ offer. The subscription continues until it gets canceled. You may cancel at any time [1] [2] [3] [4]. When you cancel during the offer period, you forfeit the remainder of the offer; it then expires immediately.
How to create a new Apple ID - Apple Support including steps and options
Manage your Apple ID - Apple including account information editing and adding a payment method on the web.
Apple ID support - Official Apple Support
Apple TV+ on us: Subscription included with your plan | T-Mobile
↳ How to redeem
↳ Got questions? (FAQ)
↳ How do I redeem my Apple TV+ On Us?
To make use of your new Apple TV+ subscription, you need to sign in to the Apple TV app. Find the in-app Settings ⚙️ in the sidebar on the left, then navigate to accounts, and enter your credentials there.
Apple TV app user guide for smart TVs and third party streaming devices - Apple Support
About Apple TV+ - Apple
Apple Originals - Apple TV+ Press
List of Apple TV+ original programming (episodic/series) - Wikipedia
List of Apple TV+ original films - Wikipedia