Mochi IS a Japanese dessert that became popular in the Heian period (794-1185) but was mentioned much earlier in literature and government edicts.

“In the Fifth Century AD, in Fushimi, near Kyoto, we find Hata no Irogu (????), a chieftain of Korean descent, head of the Hata clan using mochi to test his skill at archery. ”
“During Prince Shotoku’s regency, (573–621) people went so wild about mochi that he had to publish an edict to stop the extravagance. ”
“By the Heian period, (794–1192) mochi was frequently used as ‘Food for the Gods,’ in Shinto rituals by the aristocracy.”
(source: http://www.discovernikkei.org/en/journal/2009/12/31/mochi-food/ )

A more general article:
“Japan and Korea both have similar pounded glutinous rice foods, known as mochi and tteok, respectively. The exact origin of mochi is unknown, though it is said to have come from China. The cakes of pounded glutinous rice appear to have become a New Year’s treat during Japan’s Heian period (794-1185)”
(source: http://www.newworldencyclopedia.org/entry/Mochi)

You might be able to make the argument that mochi originated in China, but I do not think you can make the argument that mochi originated in Hawaii. The method of making mochi using rice flour rather than whole sticky rice that is ground in the mochitsuki ceremony (which I have observed in Japan) could possibly be a Hawaiian adaption, but I have not researched this. Further- I lived in Japan for several years and did not often see mochi in many Japanese restaurants. They are sold at most in sweet shops or in grocery stores.

Hawaii has a large Japanese population and has been influenced greatly by that culture. I’m sure that many customs were refined or developed there, and I certainly appreciate the fusion foods that have developed. However, mochi has a long and well-documented history in Japan that would support my understanding of it as a Japanese tradition. Mochi is also a Japanese word.

-Sea