Hi,
The access level you add to a list determins which of your Acymailing users have access to. It's not in any way related to your website visitors.
To control what your website visitors see you should create several subscription modules that are tied to a Joomla access level. You can create one for access level guests which contains only your public lists and you can create a second one which is available for logged in users that match your ST Holder access level. yYou can create as many subscription modules for different access levels as you want.