I'm comfortable with the assumption that the drone operator was close enough to the drone to discern betwixt a gun discharge and other loud bangs. It does say they were focusing the drone on a house under construction (and even if they were flying all over the neighborhood, they would still likely end up keeping a short distance to the drone).

Edit: I'm also comfortable with the assumption that the police took the location of the firing and such into account when they made the arrest.