HONG KONG—In the years leading up to the city’s 1997 return to Chinese rule, Hong Kong citizens headed overseas by the hundreds of thousands, spooked by Beijing’s crushing of student protests in Tiananmen Square and fearful their freedoms would be trampled.

They moved to Canada, the U.S., Australia and elsewhere to start new lives, or to obtain second passports as an insurance policy should they wish to flee. Many native Hong Kongers returned, as the transfer of sovereignty came and went with few signs that Beijing was flexing...