It is much more simple and could have been done in this case (in fact the U.S. government issued the warning but no one listened). It is known that when you have an earthquake of over a 7.5 or so magnitude, there might be a tsunami. Issue warnings based on that. It is not a big deal to keep people off the beaches for a day or two.
As a biologist, I don't think your animal sensor idea would work, is not cost-effective and could be highly inaccurate
without better understanding of animal behavior.
We wouldn’t even have to do that. At 500 mph, it would travel the ocean in less than half day. A warning could let distant people know of the possibility and a watch could get the people off nearby beaches or distant ones of waves actually hit shore anywhere.
I think that a generation of people are now better protected just for knowing what to do if water recedes.