I think trying to emulate a built in browser notification is the wrong way to go. I wouldn't have got as concerned if the popup looked more like a web page overlay, with wording along the lines of:

"Hi we're from Browser-update.org (clickable), and this site has asked us to check your browser version. Your browser version is out of date, and should be upgraded. Please go to your [settings] menu to update, or visit [us] for more information."

Of course, feel free to totally ignore my suggestions - it's a free world. ;)