The answer is to determine what changed on Saturday, and if it is still happening every morning, or did they just discover the bonanza that occurs when they make a racket at 4 am? Chickens are smart, but I don't think they learn that fast, and I doubt it would be that punctual. The fact that it's puctual at 4 am also seems to rule out tree branches or wind triggering the motion detector. Predators can have a puctual schedule, but a new predator suddenly showing up at 4 am would not have been ok with the dogs. However, if a neighbor turns on a light, they may wake up and get down off the roost and then get caught on the floor in the dark when they turn the light off. Chickens don't see well in the dark, so they might panic as they bump into each other in the dark trying to find the roost. If they can't see, they're likely to think they're bumping into something that's trying to kill them, and react accordingly, which frightens everyone else in the coop even more. Sort of like Henny Penny, except instead of thinking an acorn is the sky falling, they think that coop-mate they ran into is a predator, scream bloody hell about it and everyone panics.
You may need to quietly go out with your dogs around 3:45 am and sit in the dark and watch and listen. If you don't see or hear anything before they start making a racket, then I agree that there may be (or was the morning this started) something in the coop that's startling them. I'm just not sure mice are that punctual, but maybe they are. Are snakes punctual?