I think you've got it backwards. Lockdowns existed before vaccines did. So people in China tend to think "you don't need vaccines (and risk side effects) when lockdowns work".

A similar notion existed in Taiwan until they got overwhelmed by Omicron. Lockdowns worked and they were able to keep COVID out of the island, so people weren't interested in vaccines hence low vaccination rates.

Western societies view lockdowns as draconian human rights violations, and don't take COVID very seriously relative to "freedom", but not all societies look at things that way. Chinese people are very afraid of COVID, much more so than westerners, and see lockdowns as an inconvenient but absolutely neccessary measure. Chinese society values responsibility more than freedom.