I bet it had to do with the 2003 SARS epidemic in Hong Kong, as is also the case in other nearby Asian cities/countries like Taiwan and Singapore. I'm from HK

I bet it had to do with the 2003 SARS epidemic in Hong Kong, as is also the case in other nearby Asian cities/countries like Taiwan and Singapore. I'm from HK and to the best of my memory the practice never existed before the epidemic. During the epidemic, anywhere you went in public, there were at least 8/10 people wearing masks, thanks in part to huge public (TV/print) campaigns by the government and places like schools/clinics/hospitals providing free masks. That is just one of many counter measures that live on to this day. Another one is that all elevators and escalators have stickers or signs stating how many times/day and when it was last disinfected, and elevators tend to have a big clear plastic sheet covering all the buttons.