AJAX all-time returns the content for the not logged user

I’m doing Ajax authorization for WP. Principle is simple:
On Ajax login or logout WP returns the current html page (only body tag) for logged (or vice versa) user. After that, existing html is replaced by JavaScript.

For some reason, when entering or exit Ajax always returns the page only for NOT logged user, regardless of whether the user is authorized.

is_user_logged_in() always returns false.

Can you please tell where could be the problem? Thanks