Quebec has no say in regards to family reunification and protected persons (refugees), it’s a federal responsibility. There is nothing in the Canada-Quebec Accord that mentions these two streams.
It’s an IRCC’s (and probably current administration) decision.
Here is the refugee section in the Accord, read section 20.
Refugees:
17. In accordance with its international obligations, Canada shall determine who is a refugee within the meaning of the United Nations Convention Relating to the Status of Refugees, and who are persons in similar circumstances in need of Canada’s protection.
18. Subject to section 20, refugees and persons in similar circumstances identified by Canada who are destined to Québec and who meet Québec’s selection criteria shall be admitted by Canada if they are not members of an inadmissible class under the law of Canada.
19. Subject to section 20, Canada shall not admit a refugee or person in similar circumstances identified by Canada who is destined to Québec and who does not meet Québec’s selection criteria.
20. Where permanent resident status is granted to a person already in Québec who is recognized as a refugee, Québec’s consent shall not be required.