IIRC, when the new ASC was first launched, just like with the old AD users were logged out when they quit the browser, but not automatically after a period of inactivity. The auto logout behavior appeared after a month or so, around the same time a few other changes were made, like including location info under a user's avatar in replies.
The period of inactivity before auto logout is triggered is not fixed. Usually, it is around 30 minutes but at times it is substantially longer. (For example, on at least one recent occasion, I was surprised to see that I had not been logged out after about 2 hours of inactivity.)
I suspect this variable logout behavior is related to the load placed on the ASC servers by logged in users. Each logged in user requires a certain amount of server-side resources to generate "on-the-fly" things like user-specific lists of new-to-them content, customized home page views, & so on. Supposedly, the site had to be switched to the newer version of the site software because the old version's outdated server management system could not keep up with the sharply increasing use of the site.
So my theory is that the new software purges inactive user sessions from the servers when the load reaches some critical point to prevent them from overloading.