In order for Advanced Access Manager to control which user roles can access the Spider Calendar we would need to know what capabilities you have coded into Spider Calendar that allows the Admin to see the menu that other users cannot.
I have been unable to determine which capabilities you are using as there do not seem to be any which clearly relate to spider calendar.
Is it possible that you are using some other method to restrict who can see the calendar menu? Can you tell us how you are doing this so that we could show the menu to all users and then restrict access to it using AAM please?
Thanks