To me a storm window isn't the actual house window. It is an accessory. I would have included the actual window sashes plus the storms. Your painter should have explained exactly what will be painted and included this description on the contract before you accepted it.
When I'm looking at a house, I ask questions like "Do you want the actual window painted or just the exterior surface of the storm?" Walking the home with my customer and seeking this kind of info should be a natural part of the bidding process.
I just finished an old home that has solid wood storms. The storms were removed and the actual windows plus the storms were prepped and painted. The storms were then reinstalled.
There isn't a standard way to bid a paint job. It is up to your painter and yourself to understand each others expectations before the painting begins.