Please don't start a sentence in the subject and finish it in the comment. It makes it harder to quote your post for context.
I can think of three kinds of interstitials, each with a different set of who pays and who earns. For ad interstitials, the advertiser pays, and the ad network and the "publisher" (site on which ads are placed) earn. For stickiness interstitials, such as follow us via e-mail or Twitter or download our app, the same happens except much later when the user visits again later and views more ads. For subscription interstitials, the user has to pay to make the box disappear.
tab close an if the "do you really want to do this"
I've seen this with "1 weird trick" clickbait ads that lead to a 20-minute video infomercial with no progress meter. Click the back button or close box, and they will replace the video with a transcript and put up an "are you sure" to let the viewer choose to finish the ad in case the viewer prefers text to video.