In 2013 I published a paper with my Université de Sherbrooke colleagues, Luc Godbout and Suzie St-Cerny. Luc is the chair of the centre for research on tax policy. Our paper shows that in 2008, as a result of the Quebec system having generated much higher labour force participation among Quebec mothers, the federal government had cashed in $650 million. Overall, the two levels of government got $900 million in associated tax revenues that year, 2008.
Of course, the $250 million that Quebec got was net of what it had to pay for the system itself. In other words, the federal government doesn't pay a penny for that system, but cashes in everything. There is no absolute necessity that the federal government return something to the population, to the province, or to the system, but it would seem more fair if the revenue coming from more mothers being in the labour force were shared between the two levels of government.