CAQ keeps promise to cut immigration

The CAQ is keeping a key campaign promise to cut immigration by 20% next year, even though Justin Trudeau has quietly pointed out that the province is already suffering from a shortage of manpower.

I’m curious. Quebec not being a sovereign nation, how does it impose its own immigration rates? Is there any barrier if someone who comes to Canada moves to Quebec later? Although with an attitude like this in place, it’s hard to see why they’d want to.