Problem solved. I talked with my hosting, and the cache they are using was cleaned after that, and not any more existing problems.
This may stay as mystery. Looks like everything is ok on pages, but the result remains.
One more detail. If I modify menus with “Manage With Live Preview” it looks good and exactly as it should be. However, when trying real live then nothing has changed. I even installed one new browser to block any kind of cache things but it’s there too.
