This demo hilights a couple of new options (as of 5.6.5) namely 'default tab' and 'remember last open tab'.
The 'default tab' option allows you to change the initial tab that is opened the first time he visits the page. The default tab number to open is still tab 1. On this page there are two modules with the same content. On one the default tab is set to 2 and on the other the default tab is set to tab 3.
The 'remember last open tab' option allows you to change whether or not the last opened tab is remembered across page views. The default value for this option is to remember the last open tab. This means that when a user leaves the page and comes back, whichever tab they were viewing when they left the page will be reopened when they return. You can turn this option off by unchecking the option in the setting screen. On this page the last module has this option turned on and the top two have it turned off. Try selecting various tabs and then move away from this page and come back to it to view the full demonstration.