Domain Mapping Cross-domain autologin question

Hello,

I have a question with regard to domain mapping on a multi-site subdomain-based network. I have "Cross-domain autologin" set to "Yes" and "Load Cross-domain autologin asynchronously" checked.

When a user logs in to subsite1.mynetwork.com, should they also be logged in to http://www.mynetwork.com? It doesn't appear that they are. Specifically, here's what's going on.

I go to subsite1.mynetwork.com and I log in with User1. It takes me to subsite1.mynetwork.com/wp-admin. I then go to the address bar and type in http://www.mynetwork.com and it shows that I'm not logged in. If I log in again on http://www.mynetwork.com it then shows the admin bar at the top. I'm not sure if this is behaving as expected or if some other plugin is conflicting with the expected behavior.

Can you describe the expected behavior for Cross-Domain AutoLogins on Domain Mapping?

Thanks,
Dave