This is just my semi educated guess.
I would guess they can tell by the wattage use and the “startup” profile when the voltage jump hits the meter.
For example then might know that most residential refrigerators use 900 watts, but have a startup load of 1300 that last 2 seconds, where as an electric dryer uses a small startup load, but an “on again off again” load of 1,200 watts as they can see the heating elements cycle on and off.
So long as 2 appliances don’t start up at exactly the same time I would think they could be fairly accurate guessing as to what turned on or off.