You mention microwaves, they are a concern as the frequency used is absorbed by water (that's why it works to cook), so there are regulations about how much power can be output in these ranges. Same thing with cell phones -- lots of interesting things about how they test SAR, which is basically how much radiation your head will absorb with a phone upside your head.

This article makes it sounds like they use 5 GHz 802.11ac (https://gigaom.com/2014/03/12/vivint-will-use-a-gigabit-wi-fi-mesh-to-power-its-utah-home-broadband-service/) which isn't around the 2.4GHz microwave range.

I'd suggest you just ask them. I'd think they'd have some information available they provide to people with concerns.