How to add a payment method without it being charged for your subscriptions

You cannot prevent that other than either ensuring you have a second payment method you can move to the top position when it is time to pay for a subscription, or by ensuring you have adequate personal balance in your Apple Account to pay for items (even that may not stop it*).

How App Store and iTunes Store purchases are billed. Click here --> How apps, content, and subscriptions from Apple are billed - Apple Support

"Which payment method is charged?

When you buy items or pay for subscriptions, Apple automatically attempts to charge your payment methods in this order:

1. Apple attempts to use your Apple ID balance to cover the full amount.

2. If you don't have Apple ID balance, you don't have enough to cover the full amount, or an item cannot be paid for with Apple ID balance, Apple attempts to charge your primary payment method (typically a credit or debit card, but varies according to country). The primary payment method is at the top of the list in Settings on your iPhone. You can control which payment method is at the top of the list.

3. If there's a problem with the primary payment method, or if the primary payment method can't be charged for the full remaining amount, Apple attempts to charge your other payment methods in order from top to bottom. If none of them can be charged, Apple may try again.

*How apps, content, and subscriptions from Apple are billed - Apple Support

Some purchases aren’t charged to your Apple Account balance

- If you're in a Family Sharing group, purchases that you make are charged to your personal Apple Account balance. If you don't have enough Apple Account balance to pay for the purchase, the remainder is charged to the family organizer if purchase sharing is turned on.

- You can’t use your Apple Account balance to buy gifts or gift cards.

- Some subscriptions might not be charged to your Apple Account balance.