First off, it is very early for you to be worried about your post operative result, whether this is an insurance case or a cosmetic case. Wait at least 3 months before worrying about your results.
However, some information for you to digest while you wait: As your insurance covered your first eyelid surgery [blepharoplasty or ptosis repair?], it means that it was a visually significant problem. The goal of that surgery is to remove the excess eyelid skin [or raise the eyelid via ptosis repair] so that you can see better [improving your visual field]. Your insurance will cover the surgery because it is a medical problem.
Now the surgery does have an added bonus of improving ones appearance, which patients enjoy. It is an added benefit for the patient, and most are very appreciative.
In these cases [insurance covered], your surgeon is under no obligation to revise your surgery unless your vision is still significantly affected by additional droop or excess skin. And there are very strict criteria set forth by insurance companies that defines exactly what "visually significant" means. You should also be aware the compensation surgeons receive from insurance companies is a significant discount from cosmetic fees. And as such surgeons would lose money by doing "pro bono" surgery for cosmetic reasons!!
When this procedure is performed as cosmetic surgery, surgeons may sometimes offer revision surgery at a discounted rate to unsatisfied patients in which they feel revision is beneficial and reasonable. Again they are under no obligation to do so, since as surgeons we know that we cannot guarantee results, or patient satisfaction, and this is discussed in the consent forms of most cosmetic surgeons.
I hope this explanation helps.