Will fat that is placed high shift down into the lower buttocks after bbl?

Your PS is absolutely correct in saying that your results will look better when the swelling goes down and everything settles in. I don't necessarily think that the fat shifts from the superior aspect of your buttocks to the lower buttocks, but the shape does tend to round out during the healing process. Try to be patient...plastic surgery has a big component of delayed gratification. 

At just 15 days post BBL surgery, you are probably still swollen and it will take another 4 to 6 weeks to see the final result.  Although, the injected fat shouldn't shift position significantly, the decrease in swelling and relaxation of the skin should result  in causing the area of fullness the move somewhat lower.  Give things time to settle. Best wishes, Dr Lepore.