I thought the implication was that many comet fragments impacted earth in both periods. Thus the coastal living peoples were affected by the tsunamis and the inland peoples were little impacted. Except for genghis khan, who saw one of these meteorites as a sign to conquer his southern neighbor, China.
I am assuming there is no record of a major tsunami in Japan or China at this time, if for no other reason than it would get mentioned. Especially since there is a rather strained mention of a typhoon four years later..
That leaves us with coastal peoples in the Middle Pacific Islands and the Eastern Pacific coasts .. and New Zealand. I don't have that much problem with the idea of comet fragments explaining the cited events there; my problem is with the idea that this could've reached the scale required for global climate change.
You cannot alter the El Niño system, typhoon/monsoon patterns, and Eurasian temperatures without an extremely dramatic ground impact.
PS. I would add that a heavy bombardment of fine space debris would also cause climate change on that scale, but that is not something you could localize to the Pacific Basin. The debris would undoubtedly disperse throughout the atmosphere and create similarly notable climatic effects beginning about 1178 in Europe as well. By the way, this was the era of Saladin and the Third Crusade, and we have highly detailed accounts from both the Christian and Arab worlds.
That leaves unresolved the paradox of cooling in Mongolia but warming in the Pacific, which is what the cited events represent. I really just think there are way too many problems with the climate part of this hypothesis to make that aspect plausible.