LeoLee Polylang creates its own way to handle posts & terms that is quite unorthodox and does not really follow defined by WordPress core standards. Contacting directly with the plugin owner to implement some sort of integration between two plugins, was not received with much interest, so I've deprioritized this direction.
Probably your best way to manage access to your content with Polulang installed is to define access controls while editing posts or terms. AAM renders additional metabox "AAM Access" that you can use to set desired access settings.
Keep me posted.