Just in addition to above I would like to add that contractor fixed the problem. He found leak between bathtub and drain flange exactly as it is shown on my picture with the arrow. It looks like bathtub bottom surface where gasket is was rough and the gasket itself was very stiff. So he changed that black gasket and applied some plumbing putty to seal the gap. Now everything works fine.
Also I have found an interesting discussion on this topic here: