For better location tracking Wi-Fi should be ON!
Wi-Fi locates indoors with accuracy of 20-50 meters.
Google, as a location service provider, collects location data by publicly broadcasted Wi-Fi wireless access points, as well as GPS and cell tower data. KidControl app can use this data. And it is not necessary to log in with a password to a wifi router. It is simply enough to have wifi turned on and to be in the coverage area of a wifi router.