When you pay online, in person or by phone, your payment is considered "accepted pending settlement", and your account is in good standing on that same day. There is one exception to this rule: if you pay in person or on the phone with the assistance of a CenturyLink agent on a weekend or federal holiday, it will be considered accepted the next business day.
If you pay by mail, your payment should be accepted pending settlement within 10 days of the mailing date.
It usually takes 3-5 days for the payment to be fully settled with the financial institution from which you made your payment. But don't worry; as long as the payment got to CenturyLink by your due date, you'll be in good standing while the payment settles