At least to laypeople, the word 中国系 only means someone who are directly related to People's Republic of China in the last few decades.
I have never regarded ordinary Malaysians and Singaporeans as 中国系 (edit: this was misleading considering the fact that Singapore is ethnically quite heterogeneous). The same is true for Koreans and Japanese, and calling them 中国系 can be offending. アジア系 vaguely includes Asian people in general.
In pure archaeological/biological contexts, 中国系 might mean something different, but perhaps such a topic does not belong to this site.
EDIT: Let me elaborate... Unsurprisingly, saying 日本人と韓国人は中国系だ basically means "All Japanese and Korean people are 中国系", and that's a bit puzzling sentence. I would assume you are talking about the origin of Japanese people (who actually came from Asian Continent more than 10,000 ago during the ice age) in an archaeological context. But when you refer to this fact, it's better to say 中国が起源だ, 日本人の起源は中国大陸だ or something like that to avoid confusion. I'm not really sure how the word 中国系 is usable by experts in such a context.
10,000 years is very long, and most Japanese people regard themselves simply as "native" 日本人 or 日本民族, not as 中国系. Japan has very often been described as 単一民族国家 which consists of "native" Japanese race (i.e., ignoring Ainu, which are small in number). Therefore, at least in non-archaeological contexts, 日本人は中国系だ sounds puzzling, or it can be even offending (perhaps like saying "Canadians are Americans" out of nowhere). If you say 日本人の〇%は中国系だ or 日本人の一部は中国系だ, that would mean something totally different and reasonable. Such a sentence safely refers to a group of people who have moved from China to Japan relatively recently after the Meiji period and have Japanese nationality.