Last I checked, in Quebec specifically, 25%+ of the population is 65 and up, and it's trending upward. Immigration rates definitely have to do with the shorter-term issues, but this has been going on for decades at this point.

Would that not make the situation worse? I would think that having more older people as part of the population means less productivity and a much bigger strain on the health care system.

I don't know what qualitative framework you are using to judge "worse". I am only remarking that increasing longevity is a non-negligible contributor to population. The process involves births and deaths, so you can't look only at births. You have to look at how many people are dying at what ages.