Its called the law of physics but you can look for Sedan Plowshare (less than 1 MT and I think it was a little more than 100 KT and displaced 11000000 tons of soil) for more information. Underwater experiments with nukes have been shallow water experiments to reduce tsunami like events.
http://www.youtube.com/watch?v=uRPXQO43ASo
I'm sorry, there is just no way that a controlled lower scale nuclear explosion a mile underwater 50 miles off the coast will produce any tsunami wave. The most relevant information I could find was from the wiki page of Moment Magnitude scale:
A rule of thumb equivalence from seismology used in the study of nuclear proliferation asserts that a one kiloton nuclear explosion creates a seismic signal with a magnitude of approximately 4.0.AFAIK, the size of a tsunami-creating earthquake is usually in the magnitude of 7-9 on the Richter Scale. This is the best I could find. The energy created from an earthquake of this magnitude is much much larger than the energy of a nuclear blast. As helpful as learning about the laws of physics and that pretty youtube video you sent me was, I'd like some additional sourced information that would explain the catastrophic tsunami you detailed originally.