I've seen a few board or card games that use an app as part of gameplay, and they fall into two categories: ones where all players must interact with the app (for example, everybody has to touch the screen to signal "I'm done" in a turn), and ones where a single player uses the app to drive the game. Which type is Mansions of Madness? It sounds like the latter from the descriptions I've found (including Board Game Geek), but I prefer information to guesses.
The reason I ask is that I don't use electronics on Shabbat, and I'm trying to plan my schedule for a boardgame convention. More broadly, I know a few people who would be challenged to use an app running on a phone because of either vision or mobility issues, and that's something I would want to take into account when planning a game with such players.