TML and Nav Menu Roles

I have a website with the TML and the Nav Menu Roles plugin. My main menu consists of pages for logged in and logged out users.

In the TML plugin I checked the checkbox for automatic log in after registration.

After registration of a user there is indeed automatic login of a user, but the menu does not react to the automatic logging in. It is only after manually logging in again it adapts to the logged in users.

Some kind of integration of both plugins is needed. Maybe this exists, I do not know.