Most of such adware has a "sleeping" timeframe embedded in it to make it harder to track the source. You won't see a popup the minute your computer gets infected. Instead, you'll start seeing them days or even weeks later.
One of the larger popup companies out there even publicly states that the target machine won't display any of their popups for two weeks after the installation of their adware.
That particular company bundles adware with free games, wallpapers and screen savers. And the reason for the two week delay is to prevent people from putting 2 and 2 together and figuring out just how their computer got infected in the first place.
So if you see such fake antivirus popups while browsing this board (or any other legit site), chances are your computer was already infected with adware some time ago.
In other words, trying to "time" it to visits of specific sites/pages/search keywords/e-mail messages is not going to be very useful in figuring out where the adware comes from.