How are new payment methods added to a subscription?
Short answer
Through the hosted payment page only. The subscriber enters the new method there, and it is saved to their record. Each subscription stays bound to one payment method, and there is no default method shared across subscriptions, so every change is a deliberate one.
In detail
Through the hosted payment page only.
Hosted payment page
New payment methods are entered and saved on the hosted payment page.
One method per subscription
Each subscription is bound to one saved method, with its expiry date visible.
No shared default
Changing the method of one subscription never changes another.