I removed your image since it displayed your email address, in two places. You can edit your copy (hiding your addy) and repost it if you like. It's not required, however. It looks a lot like mine. I do allow the OS to update System data and security files.
For info to others, the dialog showed only one checkbox ticked: "Automatically check for updates" Since it does that checking, it will also send a Notification telling you if it has found an update. You may have accidentally clicked the wrong button in the notification. It's very (too?) easy to do that.
There will always be a Flash Player item in the System Prefs, as long as you don't uninstall everything. There is also a tab you might check called "Updates". The default setting (by Adobe, of course) is to 'Allow Adobe to install updates'. Just another area to un-check, IMHO.