This term is almost exclusively used in formal political and media contexts concerning Hong Kong. You won't hear it in casual conversation about food or movies.
Official Government Statements: The Chinese and Hong Kong governments frequently use the term to assert that the “One Country, Two Systems” policy is being successfully implemented. In this context, it has a formal, reassuring, and definitive tone.
News and Academic Analysis: Journalists, scholars, and political commentators use “港人治港” as a key concept to analyze the state of Hong Kong's autonomy. Here, its use is neutral and analytical.
Political Activism and Protests: For pro-democracy activists and supporters, the phrase is a powerful rallying cry. When they use it, they are often implying that the promise has been broken or is under threat. It carries a strong emotional weight, signifying a demand for “genuine” autonomy and the right to elect their own leaders without interference.
Changing Connotations: In recent years, Beijing has introduced the concept of “爱国者治港” (ài guó zhě zhì gǎng) – “Patriots Administering Hong Kong.” This is presented as a necessary condition for “港人治港,” effectively stating that only those deemed “patriotic” to China are qualified to govern. Critics see this as a significant reinterpretation that severely narrows the scope of the original promise.