I just started a one month free trial due to my iphone 12 purchase recently. I use one of my apple device to watch movie on the 1st day. Then continue to watch the next day with my iphone 12. Do I have to pay from my apple account? Why?

I feel like there are some information missing from this question. Are you talking about a Apple TV+ subscription? If so, you can watch any of the movies/shows from Apple TV+ without paying. You may have to provide billing information just in case the subscription goes over to the following month.

If you were talking about renting a movie, then the rental is not dependent upon the device that you watch it on. You can pick up where you left off on a different device.

Most Apple subscriptions automatically renew unless you cancel them. If you cancel, you can keep using the subscription until the next billing date. If you cancel during a trial period, you might lose access to content immediately

You have to sign in on your new device first. You can't sign on on another device.

"Get Apple TV+ free for one year." - Click on the link and read it, including the FAQ at the end. --> https://offers.appletvapp.apple/