Multisite and Membership- relationship between main site and template sites

Hi! I am using Multisite and Membership. I have a main site set-up for the general public- so visitors should be able to see every page. My subdirectory sites should be private except for those who are logged-in. I set the main site settings Stranger access levels to use level>visitors. On my template site I want to set the Stranger access levels to use level> None- no access to content. But when I change one the other changes. Do I have something set-up wrong? I thought I had it set-up where each site had it's own Membership rules but apparently not. Please help if you can. Thanks!