The reason why a lot of countries in Asia have less coronavirus cases is because the citizens are following the rules. Some don't even have to be told. They already knew what to do. As for other few countries in Asia, where some of the population don't follow the rules, the governments started becoming stricter, sending the people who break the social distancing measures to jail, fining them or both.
https://www.scmp.com/week-asia/health-environment/article/3080764/coronavirus-lockdowns-are-not-reason-hong-kong-and?utm_content=article&utm_medium=Social&utm_source=Facebook#Echobox=1587424521