There are 3 things to consider, each with its own specific correction. If the implants just settled high, the opening up the capsule and repositioning them lower will help. Capsular contracture can also pull implants up, and in this situation capsule removal and replacement of the implants is usually needed. The third situation is when the implants are in the right position but the breast tissue drops over time. In that case a breast lift would be needed but it sounds like that is not your condition.
There are a multitude of causes and it takes an exam to know which cause is the most likely. But since it has been 13 years since your surgery the most likely causes can be narrowed down to two. If the breasts felt firm, it was probably a capsular contracture that was slowly occuring. If the breasts felt soft, it was almost certainly that demon, Gravity, and its effect of pulling your breast tissue down while the implants remained supported by the surrounding scar tissue.
Thank you for the question. Understanding, that without doing photographs, it is not possible to give you an assessment or advice, some general thoughts may be helpful to you. Your plastic surgeon is correct in that if a breast implant is sitting relatively high on the chest wall, it may make the nipple/areola seem somewhat low or pointing downwards. Once the breast implant is surgically positioned lower on the chest wall, the nipple/areola complex may appear to “sit” more centered on the breast mound.
Sometimes, despite a plastic surgeon's efforts, a breast implant simply does not “settle” into the dissected pocket; sometimes, the breast implant is displaced superiorly when the pectoralis major muscle is activated. Occasionally, breast implant encaspsulation (thickened breast implant capsule) may be the culprit for a breast implant displacement.
I hope this helps; best wishes with your upcoming breast surgery.