You may be using the wrong concealor, or not applying/blending it properly. It could be that you need a neutraliser (cancels out colour instaed of concealing) instead of a concealor. Book an mua for your next shoot and they will be able to advise you better than someone can over the internet without actually seeing the problem.
Certain concealors are better with different skin types. But my experience with dark under eyes (as I als have this problem), is to use a good hydrating eye cream. With dark under eyes you do need to put a little more make up on them than some who does not have them, so it is essential to hydrate the eye area, so when you apply your concealor on it does not look chalky, dry or caked in photos.