The crew of TMS is staying at the Safari Inn in Burbank, CA, which is way too far away from the fires in the Malibu / Santa Monica Mountains area (around 40 miles) to be an effective lodging zone for a news crew and as evacuation shelter.
California is three hours behind NYC so showing an update during its regular air time would mean that it was still night if not very early morning and there would not be that much daylight when they spoke to the man rescuing the dogs.