I am building stateless restfull API in Yii2. So I created new APP in my advanced app layout (as preferred by Yii2 creators) and configure all necessary things and API worked.
Finally I found out what the problem is. Yii2 worked OK, but Postman had some data stored from the past when cookies and session were enabled. What helped me was deleting browser's history (including cookies), close all instances of browser and rerun.