Is this really an idle game?

Personally, I thought idle games were supposed to progress even when you're not actively playing the app, and the fun part was opening it up to find things like 'level ups' or 'items acquired'. However, regular missions and tamer rank-up missions include objectives like 'Activate the hologram device X times' or 'Defeat X enemies', which only happen while the app is open. This means you have to keep the app running, and you can't advance to the next mission without tapping, so it's a pain to have to keep an eye on it.