The Quebec government has made a huge effort over the past decade or more to make the province a supportive, friendly place for young working parents. Accessible, inexpensive childcare, widely available after-school care and improved and expanded parental leaves have helped convince many couples that both parents of young children can work. Not as much has been done for stay-at-home-parent families unfortunately, but all the same the net result of policy choices and other factors has been a higher birth rate.
I'm not sure how the above encourages couples to have more children, but I can imagine how such pro-working family policies might attract professional thirtysomethings to Montreal. But the article goes on to explain that retaining talent is still a big problem. Being a "friendly place for young working parents" isn't enough of a reason to stay put.
Actually, I doubt out-migration is to blame for slow population growth. Attraction is still the name of the game and even the secondary migration of immigrants is far from unusual. If the pro-family policies of Quebec are better than that of other provinces, then the policymakers need to figure out how to effectively broadcast that message to the most desirable demographic. Furthermore, Quebec has a reputation as being hostile towards Anglophones. Undeserved or not, that's a barrier to in-migration. Quebec is no Saskatchewan. I also suspect that Quebec would rather hold onto native Quebecers and maintain some semblance of cultural integrity.