Did Singaporeans and Malaysians immigrate from China before?

Both Singapore and Malaysia are multi-ethnic societies, with indigenous people. In early history, there were records of immigrants from Chinese mainland, India, Indonesian Islands and continental Europe. Now they have integrated into the local society and become a local ethnic group. They are already Singaporeans or Malaysians, which raises the same question. Did Korean and Dai people in China immigrate from South Korea and Thailand to become China people?