I'm trying to get the 1 year free subscription with my new phone. When setting up it says that starting now I'll be charged $4.99.

Hello wozdaddy,

This document from Apple describes some of the terms for the offer. https://www.apple.com/promo/pdf/EN_US_ATV+_Promo_TandCs.pdf

I am curious if you are attempting to activate the offer before activating the new iPhone?

You definitely should not be purchasing a subscription. Somewhere in the Apple TV App you should see a link or message reminding you about the offer for up to three months if you have activated your new iPhone and signed into your Apple ID.

• "Offer must be claimed in the Apple TV app within 3 months after first setting up your new device. To see the offer appear, you will need to sign in with your Apple ID on your new device."

I hope this helps.

Read here if you have trouble redeeming: If you can't redeem your promotional trial of Apple TV+ - Apple Support