Tsunamis are not giant walls of water like what you see in disaster movies. They're more like an unending tide: the water just keeps rising until it floods the area. Anything floating loose on the water at the time is at risk of being carried inland, but is unlikely to be completely destroyed.

A floating data center barge anchored a mile offshore is as close as you can get to tsunami-proof. At worst, its connection to the mainland would be severed if the tsunami destroyed the local land-based telecom infrastructure. Any data located on the barge would still be intact until communications could be restored.

No more Hollywood movies for you. The only "tsunamis" with "waves" hundreds of feet high are created by cliffs or glaciers collapsing. And even then, the wave height is really the run-up against another cliff or mountain. Such waves can be dangerous to boats in confined waters, such as a bay. In the open ocean, tsunami waves are mostly harmless and even barely noticeable to boats. And all this is moot because the slip-strike motion of the San Andreas fault doesn't produce tsunamis that I've heard of.

The wave of a tsunami remains under water, until it hits the coast and the water isn't as deep as the wave is high. If you are far enough away from the coast, a tsunami has no effect nor will you notice it unless you have the equipment necessary to detect it.

The worst thing a tsunami could do to a floating data center is break the internet connection, assuming a cable is used.

just to slightly build on the other comments, I believe this barge is designed to be out from shore quite a way, if it was right up against the shore I could see this being an issue.