@vasyl My particular case is that the administrator is the only user allowed into the WP Dashboard where he is supposed to do specific tasks quite often. At the same time he should be able to do other tasks in the web application that is consuming the REST API. With the current issue the administrator will have to keep login out and login in as he switch from the WP Dashboard to the WAPP.
It seems that this other plugin was having the same issue but according to thread the got it fix.
Maybe the solution will be a filter that prevents the default authorization method if a token authorization is present in the request. Even better, this filter could be an option that must be activated within the configuration of AAM and this way we do not break the default functionality of WP unless it is necessary by the developer.
Let me know what you think about it.