As well as customer.subscription.created
you will also receive a invoice.created
followed by invoice.payment_succeeded
(or invoice.payment_failed
)
From the documentation:
If you are using webhooks, Stripe will wait one hour after they have all succeeded to attempt to pay the invoice; the only exception here is on the first invoice, which gets created and paid immediately when you subscribe a customer to a plan.
So, this means, invoice.created
event will also fire next month.
Stripe will then wait an hour before charging the customers card, then firing charge.succeeded
(if the charge is succeeded) or charge.failed
(if the charge fails)
The hour wait is to allow invoice items to be added to the invoice if you so wish.
See my answer on this question for more information on why you might need to do that...