When does the plugin actually update

At this moment, my WP site says I should update to 4.1.2. Advanced Automatic Updates has not as yet updated WP to this version. So I am curious as to when the plugin will do the update. I looked thru your support issues and found: Update Time and Interval – https://wordpress.org/support/topic/update-time-and-interval which indicates: The plugin uses WordPress’ built in update checks, which occur approximately every 12 hours. Since my WP site is aware that it should be updated to 4.1.2, it has recently done an update check. If the plugin uses the WP core update check, and this check has been performed, then the plugin should have updated the core to 4.1.2. But it has not. This security update fixes an issue where an anonymous user can take over the site. Since this issue has now been published, hackers are aware of the vulnerability and hence my site and I imagine many others, are vulnerable. Since this is an important security update, I am wondering if I should do a manual update, or in general, let the plugin do it. But I do not understand when the plugin will do it. Please explain. Thanks ahead of time. https://wordpress.org/plugins/automatic-updater/