The correct answer to your question is that you should seek out a surgeon who has devoted the time to learning how to treat malar bags, and has the surgical judgment and skill to achieve reliable correction of this problem, regardless of his specialty. The important point here is that malar bags are not a simple problem to treat. There can be a number of contributors to the problem of malar bags, and the anatomy of this area is complex. Because the etiology is usually multifactorial, the optimal treatment of malar bags will generally entail a concert of coordinated surgical maneuvers, rather than just using "the same hammer for every nail."
This can include resection of pre- and post-septal fat, release of the arcus marginalis (the attachment of the orbital septum to the bony orbital rim), septal reset (a repair and reinforcement of the orbial septum), fat transposition (movement of fat from one compartment of the eyelid to another), lateral canthopexy or canthoplasty ( techniques to tighten the lower eyelid), orbicularis suspension (tightening of the periocular musculature), fat grafting (placement of fat harvested from other parts of the body into the lower eyelid and cheek to change their contour), skin excision (including direct excision of the malar bags in some severe cases) and endoscopic midface lift. Malar bags are a complicated problem to treat, and often require the surgeon to utilize multiple approaches from his surgical armamentarium in a concerted fashion to achieve optimal results.