I had the same problem, but I got it to work by whitelisting Gmail in the block this app (to my knowledge, there are no ads in Gmail anyway, so whitelisting doesn't really matter). Do take care to whitelist Gmail, then stop and kill the block this app and restart it again, otherwise it won't work.
@colinjeavons you have a virus on your phone. Definitely not related to this app. You need to factory reset your device and start over. Also quit going to shady websites. The reason you noticed it this time is because normally that action of "taking over your device" was hidden behind all the pop ups.
Ewww, Firefox. I can't stand Firefox anymore. Plus, I use gmail and Chrome just works better for that with Chrome. Firefox has just gone down hill for me for last 4 years. Try it out and works for you, then good.
I think the app is going into standby mode in marshmallow 6.0 OS. Here is an indepth article about that, Doze, and where and what settings to adjust. Let us know if that works, and make sure you have the setting in the Block This app set to restart on boot as well. http://www.howtogeek.com/242834/how-androids-app-standby-works-and-how-to-permanently-stop-apps/
Also, when you find battery optimization settings page, be sure to set "VPN Dialogues" to "not optimized" as well as the Block This app.
One thing though, on TuneIn, you will hear the regular ads broadcast during a radio program. But the extra pop ups, and banner, and streamed audio before a show plays, ALL gone! BTW, I do have a slightly older version of the current app, because I make copies of them before updates, just Incase I need to revert because of a broken update, and or, the update adds something I don't like. It's a good practice to get into, but wish I would have saved the ones that came with my EVO 4g LTE. Anyways, the practice helped me just the other day on a broken app update (- :