Ashod,
The email option provided by the plugin is completely separate from the email options provided by WordPress itself.
The email settings on the Settings > Discussions admin page, consisting of the two checkbox options in the “Email me whenever” section (“Anyone posts a comment” and “A comment is held for moderation”) are provided by WordPress and are unrelated to anything handled by the plugin. Those options are provided even if the plugin is not installed, and are not affected by the plugin when it is installed.
The plugin only provides the option “Email me whenever a comment is submitted to the site.” in a user’s profile (in the section “New Comment Emails”).
If you want the test user to receive email notifications for new comments, the user must visit their own profile (or you as the administrator need to edit their profile) to check the “Email me whenever a comment is submitted to the site.” setting.
The Settings > Discussions admin page only relate to the designated admin email address getting email notifications. (Which, again, is separate from anything this plugin handles.)
Does that help clarify things?