It's not rocket surgery
The principal false media hysteria had to do with "a tsunami racing across the Pacific." Racing, yes. Noticeable, no. NOAA, which is very good at dampening panic, has produced this fact sheet about tsunami characteristics, including their behaviour in deep water. I first hit this item in a mariners' meteorology course some years ago. On the open sea, most vessels will not notice a tsunami. NOAA says they might be up to three feet at sea; I recall learning that most of them are inches high, and undetectable at sea amongst much larger masses of wind-driven water.
The Poseidon Adventure shaped most peoples' ideas of tsunamis at sea. It was fiction.
Any wave is something like a lawn roller. It has a top and a bottom. Onshore waves form when the bottom of the roller meets resistance. Tsunamis move rapidly across open seas as an energy pulse, then slow and grow when the bottom meets resistance. Its speed is reasonably predictable. The size of the wave that hits a shore in the way depends on a host of variables, but it isn't inevitably a mountain of water. Some mainland U.S. newscasters have been inclined to sneer at the tsunami impact in Hawaii. It was modest if you expected everything up to 500 feet above sea level to be inundated. By the looks of the video, it was not so modest if you lived in a house on the beach.
It's unreasonable to expect your average Joe and Jane to be up on their meteorology. It should be reasonable to expect their news and weather to provide accurate information that draws the line between caution and panic: but it's not.