The problem wasn’t the earthquake. The problem was that the reactors require external power to operate. Fukushima didn’t get into trouble until the back-up generators quit. Someone correct me if I’m wrong, but I think they were OK immediately after the quake. Had the reactors been able to power their own control systems, they wouldn’t be in this fix.
From everything I have read the water drowned the on-site generators and the secondary hookups for truck-based generators were flooded as well. By the time they got the second set of generators connected the battery backups were depleted and water had stopped flowing.
Yup, the generators quit when swamped by the Tsunami. When that happened, the batteries cut in. They worked ‘til exhausted eight hours or so later. The plant stops producing power when it’s “scrammed”, thus the need for external power as soon as the quake hit.