A key date - Aug 31 - has become a bone of contention in a spat between activists and MP Seah Kian Peng.
He also wrote: "I am amazed that Dr Thum and his supporters should proclaim that Singapore is part of Malaysia (or Malaya)."
Freelance journalist Kirsten Han, in her response, said Dr Thum was merely stating a historical fact since founding Prime Minister Lee Kuan Yew had actually declared Singapore's de facto independence on Aug 31, 1963.
But few in Singapore are aware of this historical milestone, said Dr Leong Chan-Hoong, head of the Institute of Policy Studies' Social Lab, who led a study on the impact of historical events on national identity.
"Few in the younger generation are aware of our historical journey towards independence in 1965. For many young Singaporeans, the notion of nationhood starts on Aug 9, 1965, when Singapore separated from Malaysia. To many Singaporeans, Aug 9, 1965, was the birth of a nation and the start of the Singapore universe," he told The Straits Times.
But when history books say that Mr Lee had made a declaration of independence on Aug 31, 1963, it was in reference to independence from British rule, a move that was in line with his push for Singapore to join the Federation of Malaysia.
As Mr Toh Cheng Seong wrote in a letter in today's Straits Times Forum page: "Singapore did not exist as a sovereign entity (on Aug 31) in 1963, but as part of Malaysia. Hence, we celebrated independence from British colonialism on Aug 31 for two years as Malaysians, and not as Singaporeans."
He also said "our nation came into being as an independent city-state - from Malaysia - only on Aug 9, 1965, with all the sovereign rights of statehood which guarantee (the country) its seat at the United Nations".
To proclaim Singapore's unofficial independence day as falling on Aug 31, which is Malaysia's Merdeka Day, is "absurd", Mr Toh said.
Dr Thum had said on Facebook on Aug 31: "Selamat Hari Merdeka to the people of the former Federation of Malaya! (and happy unofficial independence day to the people of Singapore!)"
Former Nominated MP Calvin Cheng, in a Facebook post on Sunday, echoed Dr Leong's thoughts. He also pointed out another significant event had taken place on Aug 31.
That happened in 1957, when the Federation of Malaya - which did not include Sabah, Sarawak and Singapore - proclaimed independence from British colonial rule.
Mr Cheng felt that the brouhaha about Dr Thum wishing "Malaya" Happy National Day and the people of Singapore an "unofficial independence day", is due to "a lack of knowledge about Singaporean history".