The inevitable question is: So what? For starter, there is no denying that China influenced every people and their respective countries in Asia, but the question from each one of them is: So what?
Are you saying that just because we inherited/adopted some aspects of Chinese culture, somehow we 'owe' China fealty?
Here is what Lee Kuan Yew said in his memoir...
From Third World to First: The Singapore Story: 1965-2000 [Yew, Lee Kuan] on Amazon.com. *FREE* shipping on qualifying offers. From Third World to First: The Singapore Story: 1965-2000
Deng Xiaoping's China
The Malaysians must be suspicious of Deng. There were underlying suspicions and animosity between Malay Muslims and Chinese in Malaysia, and between Indonesians and their ethnic Chinese. Because China was exporting revolution to Southeast Asia, my Asean neighbors wanted Singapore to rally with them, not against the Soviet Union, but against China.
Asean governments regarded radio broadcasts from China appealing directly to their ethnic Chinese as dangerous subversion. Deng listened silently. He had never seen it this light: China, a big foreign power, going over the governments of the region to subvert their citizens. I said it was most unlikely that Asean countries would respond positively to his proposal for a united front against the Soviet Union and Vietnam and suggested that we discuss on how to resolve this problem. Then I paused.
Deng's expression and body language registered consternation. He knew that I had spoken the truth. Abruptly, he asked, "What do you want me to do?" I was astonished. I had never met a communist leader who was prepared to depart from his brief when confronted with reality, much less ask what I wanted him to do. I had expected him to brush my points aside as Premier Hua Guofeng had done in Beijing in 1976 when I pressed him over the inconsistency of China's supporting the Malayan Communist Party to foment revolution in Singapore, not Malaya. Hua had answered with bluster, "I do not know the details, but whenever communists fight, they will win." Not Deng. He realized that he had to face up to this problem if Vietnam was to be isolated. I hesitated to tell this seasoned, weather-beaten revolutionary what he should do, but since he had asked me, I said, "Stop such radio broadcasts; stop such appeals. It will be better for the ethnic Chinese in Asean if China does not underline their kinship and call upon their ethnic sympathy. The suspicion of the indigenous peoples will always be there, whether or not China emphasizes these blood ties. But if China appeals to these blood ties so blatantly, it must increase their suspicions, China must stop radio broadcasts from south China by the Malayan and Indonesian Communist Parties.
Basically, during the Cold War, China had a racist program in appealing to ethnic Chinese in other Asian countries fomenting communist revolutions. The plan failed mainly because despite genetic ties, other Asians felt they owe China shit. Nothing wrong with keeping Chinese heritage while keeping away from China. From my mother's side, I have Chinese and Indian. I owe either country nothing.