The reactors are not damaged by the quake. The three affected plants automatically shut down with an earthquake. It is not like throwing a light switch. They are hot and have to cool.
The one plant in question is having trouble generating enough electricity to run pumps for the coolant.
It's a terrible mess over there. I was watching it on tv this morn. Saw cars driving down the road and the surge overtaking them. I believe the death toll will be high. Of course one is too many. Men, women, and children........ just terrible.
There are multiple redundant systems for keeping reactors cool. There is no single point of failure.
Everything I have heard shows the plant following standard emergency procedures, including evacuation of those within emergency event perimeters.
While no doubt things are very stressful at the plant right now, this is the sort of thing we in the nuclear industry train for extensively.
Of course listening to the media would lead one to believe a reactor is about to explode.