The chain reaction can be shut down in a matter of seconds. However, the reactor continues to generate a huge amount of heat for weeks afterwards. It's not as much heat as a fully-running chain reaction, but it's still enough to cause a catastrophe if cooling is not kept running - we're talking multiple megawatts of heating here. The cooling requires an external power supply. It was the failure of this external power supply that caused the problems at Fukushima.
There are newer reactor designs that are specifically engineered to be capable of cooling themselves on shutdown without an external power supply. However, most reactors in the world do not have that capability.
The chain reaction can be shut down in a matter of seconds. However, the reactor continues to generate a huge amount of heat for weeks afterwards. It's not as much heat as a fully-running chain reaction, but it's still enough to cause a catastrophe if cooling is not kept running - we're talking multiple megawatts of heating here. The cooling requires an external power supply. It was the failure of this external power supply that caused the problems at Fukushima.
There are newer reactor designs that are specifically engineered to be capable of cooling themselves on shutdown without an external power supply. However, most reactors in the world do not have that capability.