Last summer I was playing a fun little game on my iPhone and kept causing problems for other people on the same Wi-Fi network just me. It turned out that when you dismissed a video ad is soon as possible to skip it, it seemed to keep downloading the ad anyway. And then maybe some more. I don't know, but it was a huge data hog on Wi-Fi.
If that happened on cellular (I didn't play much while out and about, and it may have changed its behavior on cell) it could've easily racked up a huge bill. And that would be the developers fault.
In the two weeks I've been playing Pokémon go my iPhone says I've used 150 MB of data. I've been looking at it a lot as I drive around (whenever I stop in a parking lot), and I often leave it running while driving (to get those fake steps when I'm going slow enough) and it hasn't done much so I don't think the game is missbehaving. Given that it seems to have to constantly reload landmarks in areas I frequent some cashing might be a good idea, but it's not too horrendous.