I'm seeing occasional rogue popups on other sites, but only on iPad Safari. The same site on my desktop does not throw these. I haven't seen any on Remote Central. As in the examples given here, it seems like an excuse to have the user click on something. I interpret these popups as an attempt to have me launch some malware. I close that browser window rather than clicking on the item. The next time that I visit the site this rogue popup may or many not appear. Usually, I'll avoid that site for a few days and the problem clears.
In my case the popup appears after I click on a legitimate navigation link on the primary site. I haven't seen any of these popups on a page where I have directly entered a URL.
I haven't looked into this in any detail, but my thought is that the primary site or one of their ad partners was hacked. I tried force closing Safari, even force closing everything, clearing the browser cache, and rebooting the iPad, but none of this will make the popups stop.
Perhaps someone is testing a malware injection scheme.