Perhaps not, but I'd expect you'd flip a switch, and then the automated systems would shut it off, or something to that effect.
You expect wrong. Nature isn't rubber padded, and technology isn't friendly magic. You flip switch, control rods go in, the chain reaction stops, the decay heat continues.
So, set it to shut down automatically after 36 hours without operator action, and it will be fine.
It is 72 hours after the full shutdown, that it melts itself down. edit: or to be pedantic, gets outside design parameters; the melt may take another couple days.
Why didn't they have that problem at Three Mile Island?
Because the spent fuel pool didn't boil itself dry. They had a core meltdown, luckily they had full external power and could keep circulating the coolant.
The Fukushima is the TMI without external power: same reactor types, 3 out of 3 melting. The Tokio being evacuated is Fukushima the other time of the year when wind is blowing inland. Ain't a safety feature of the reactor design that it failed in the season when wind is mostly blowing to ocean. At least they did consider evacuation.
Just a reminder that some of the old threats are still around (and hence that AI is not only something that can go hideously badly, but also some thing that could help us with the other existential risks as well):
http://blog.practicalethics.ox.ac.uk/2012/03/old-threats-never-die-they-fade-away-from-our-minds-nuclear-winter/
EDIT: as should have been made clear in that post (but wasn't!), the existential risks doesn't come from the full fledged nuclear winter directly, but from the collapse of human society and fragmentation of the species into small, vulnerable subgroups, with no guarantee that they'd survive or ever climb back to a technological society.