Nuclear plants have manual and passive safety mechanism that don't rely on electricity to prevent meltdowns. So not every plant would meltdown.
Not an expert in this area by any means, but thought the bulk of the passive safety mechanisms were essentially the shielding and cement domes? Does nothing to prevent meltdown, just tries to contain the radiation when it DOES meltdown. Most of the stuff to prevent the meltdown looked like it involved pumps and water to cool the reactor, and that would be a no-go in this situation.
So they may ALL melt down, and most will just be contained. For now. Give it a few years, and weather, natural disasters, plant life, etc will eventually start cracking open the ones that had contained the spill previously. Sooner or later, it won't be pretty.