Is there an order in which electricity goes off from the point of disconnection or fault?
In movies it just what looks better. In reality there is no storage for energy, so if power plant fails so badly that the other plants can't sustain supply, everything will blackout very fast. But it must really be a catastrophe, because normally it's not a single power plant, it's a network. If one fails, it is disconnected (google high voltage arc switch) and power flows from other generators.