I did the pressing once again. This time I modified shape of the chair. Now there is not little curve at the top any more. So plywood pieces are squeezed only in one place. And the result was much better. No cracks any more! Of course, thanks to wooden guys – masters of the workshop who helped with fixing ply to the mold. That was a big deal, yeah.
Such a simple thing as marking a shape of the chair also can be very… time taking.