Your domain's dashboard page shows you the renewal date as well as the next billing date.
When logged into your account, if you go to your dashboard and then to the domain's page, there's a list of information that shows the dates and domain's renewal status.
If the domain shows Renewal Date and Next Billing, with cancel to the right of Next Billing, that means the domain is set to auto-renew.
If the domain shows Expiration Date instead of Renewal date, shows renew to the right of Expiration Date, and does not show the Next Billing line at all, it means the domain is set to expire.
If the domain's renewal has been billed, but the domain's renewal date has not arrived yet, the customer will not be able to cancel the domain's renewal themselves, and the cancel/renew link will not appear. Only the green paid icon will appear.