This is to be expected. You will continue to have access to your subscription during the remainder of your current term (as indicated by the "next rebill" date). You can confirm that your subscription is cancelled if the word "stopped" appears under the "subscription" heading.
After you pass your next rebill date your subscription will no longer be active and you will no longer have access to subscription content. However, your account with us will still be active and you will be able to view your account history and re-subscribe at any time.