Actually I have the iPhone 7+ with Otterbox Commuter, and it DOESN''T work with the case on. I previously had the same issue with Nexus 6 and Galaxy S8+. The S8 had a flip tri fold case so you could get a bit closer, and it worked sometimes. Will try screen down. When I do it with the case on, the terminal responds with "please insert/swipe card" and the option to tap goes away.
You'd think it would not be an issue, but there you have it.