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The Whale was a monster, killing other whales and depriving the people of meat and oil. The Thunderbird, a benevolent supernatural being, saw from its home high in the mountains that the people were starving. The great bird soared out over the coastal waters, then plunged into the ocean and seized the Whale.
A struggle ensued first in the water, the tribal tale says. "The waters receded and rose again. Many canoes came down in trees and were destroyed and numerous lives were lost."
The Thunderbird eventually succeeds in lifting the evil Whale out of the ocean, carrying it "high into the air (and then) dropping it to the land surface at Beaver prairie. Then at this place there was another great battle."

...Whale had a son, Subbus, who took Thunderbird several more days to locate and kill. The earth-rumbling struggle persisted, but eventually Subbus was subdued.

ET battle, obviously. The Leftist Whales travelled in USOs, manipulating the flow of fish and animals along the coast to reward or punish the natives depending upon whether they served them properly. The Rightwing Thunderbird UFOs travelled in the sky, saw this lockdown, and attacked.

Due the the massive force fields and energy weapons used by these vehicles as they grappled together in their antigravity bubbles and bounced up and down upon the ocean, tidal waves and earthquakes were generated. After the Leftist USO was destroyed on the ground, some escape pod ran for it, and it took a while longer to get them all, which is why the pounding continued for awhile.

Simple.