I'm confused. Usually a "natural experiment" is a chance event that affects some random subset of a population. Here, they seem to be using "natural experiment" to refer to the event that someone decides to move to a different city. But obviously the subset of people in Amarilllo, TX who decide to move to New York, NY are going to be somewhat different than the subset who don't. So isn't this confounded?

It's really strange that they just jump into the paper and keep saying "natural experiment" over and over again without any justification that they actually have one. They do eventually get to this in the "Selection effects in relocation and mobile app usage" section, but I think they really downplay the seriousness of the issue.

I think they were claiming that people who move to certain cities increase their activity after moving, regardless of where they come from.