As you're noting, fraudulent refugee claimants often have an incentive to come here because of our generous social assistance programs. While it wouldn't be in the jurisdiction of the federal government to direct them to do so, provinces lessen that incentive for claimants to come here and abuse the system. Provinces can bring in their own measures to try to determine who are legitimate refugees as well as whether these applicants should be receiving social services. Provinces provide social assistance only to those whom they really want to. It's a voluntary act.
Provinces can do their own homework as well. They don't always have to take the federal government's word for it on who is a legitimate refugee, when we have huge numbers of people coming from Europe who are abandoning their claims to begin with. Provincial governments can check the math twice and see if they should really be providing generous moneys—not just welfare but also health care and the many other benefits that come with Canadian residence.