They also will also consider every decision in the face of Section 7 of the Charter of Rights and Freedoms which provides for a fundamental right to justice and security. If the extradition, or actions post-extradition, would likely violate the person’s rights then they will not be extradited. (So, e.g., will not extradite someone to face the death penalty.)
There’s a general overview of the process, checkpoints, appeals, etc here: https://www.justice.gc.ca/eng/cj-jp/emla-eej/extradition.htm...
Meng is being charged with fraud for lying to HSBC. It was a point of contention since the representations she made would not have been criminal in Canada (no sanctions). However the actual act of making fraudulent misrepresentations is the crime, and it's criminal in Canada as well. There's some information and a link to the actual court ruling here: https://www.macleans.ca/news/canada/with-the-meng-wanzhou-de...
Your question phrased another way:
> "Does it imply that anyone wanted by the government can be detained by the police and the government needs to establish the legality of it only after the fact?"
Yes, very much so.
I suspect if the US were randomly and wantonly requesting illegal extraditions to harass people located in Canada that Canada would simply stop making provisional arrests pending formal requests for extradition and require the paperwork up front.
On what charges was the Canadian warrant issued to arrest Meng?