Is Internet Explorer 9 an "evergreen" browser? What about IE 10?
The latest versions of Chrome, Firefox, Edge, and Safari are evergreen browsers, i.e. they automatically update themselves silently without prompting the user.
Microsoft started moving toward evergreen browsers as of IE10, the first major Internet Explorer release after Microsoft made the announcement it sounds like you are referencing. Through Windows Update, Microsoft automatically updates users to the latest version of Internet Explorer supported by their version of Windows: up to IE8 on Windows XP, up to IE9 on Windows Vista, while IE10 requires Windows 7. Technically, a user on Windows 7 with IE9 (provided they have a local admin account, automatic updating enabled) would be upgraded to IE10, but that doesn't make IE9 an evergreen browser; Vista users stuck with IE9 cannot upgrade.
Regardless, we are now most definitely in a new age of the web, where developers don't have to worry about supporting ancient browsers and can actually use the new features coming to the web platform. For what it's worth, I drew a line in the sand with a web application at Intel to only support evergreen browsers, and it makes me very happy to say so, having gone through the dark ages of supporting oldIE myself.
By "Evergreen browser", I mean a browser whereby only the latest version is supported by the manufacturer and most apps that support it. That said, no version of IE is evergreen. However, Microsoft Edge is evergreen.
To illustrate, if you have a bug or serious-issue, even in the immediate previous version, no developer nor browser-maker will fix it, IF it works fine in the latest and the browser is "Evergreen". You have to update it. On the opposite end, in like 2014, if you have a bug that occurs in IE 9 but not IE 10, the bug still has to be fixed, since both versions were within Microsoft's date of support (at that time). Microsoft or the developer responsible for the bug had to deal with multiple version of the same browser.
"Evergreen browser" has nothing to do with auto-update. That is just an updating strategy