If the Canadian government requests the United States government to detain someone, the US would. That's the nature of extradition treaties. Nobody is doing anyone's "bidding".
It's a run-of-the-mill legal process that the Chinese government has decided should have significant political implications for Canada and Canadian citizens. It's important to bear in mind that this was a set of decisions deliberately chosen by the government of China in response to Canada obeying its obligations clearly laid out in a readily available treaty.
As you so wisely and correctly note, no legal process is automatic. Yet routine extraditions, even of politically sensitive people, come quite close.