I'll be the one answering again. There's a long history behind this.
Back in the 1960s, provinces and territories had the ability to use opt-out arrangements. Quebec had an opt-out arrangement for a funding program for which they had already provided funding for 16- and 17-year-olds. Essentially, when the government introduced a similar program, they then allowed Quebec to use tax points to fund that program instead.
The program has evolved. Quebec makes annual payments to the Government of Canada, because when we expended the program to include all Canadian youth, Quebec allowed the feds to make the transfers directly. Essentially it's just a recovery that happens every year. The amount is collected from Quebec in two instalments. The first 50% is estimated in the first working day—typically April 1 of the fiscal year—and the second installment happens before the next April 1 of the next year.