I always clear my bill fully and on time. I dont even need to pay annual fees!
You are worry about any potential privacy leak, but since you mention that you have updated the contact with the bank 6 months ago and now that the phone number belongs to the bank then that should allay your concerns.
FYI, credit department will call you and hang up just as a reminder and for record that they tried to contact you for payment, this is some kind of "requirement". If that's what you are looking deeper into, then this is your answer.