OK no, the agency does not set your hours. At least, not here it doesn't. The problem is that agencies are not the same across the province. Some give providers a certain amount per kid, per meal for food, some pay providers more to include food. Some won't take on a provider with a pool, for instance, no matter how it's fenced. To ask if "agencies" in general do something is hard to answer.
As far as I am aware, agencies set fees and take a cut, amounting to anywhere between $8-$10 a day per child. As far as I know, you can take on private clients, but anyone requiring subsidy will have to go through the agency.

In my city, there are no agency providers who work past 5. That is the provider's choice, however, not the agencies. I don't work past 5 either. Some agencies give providers a lot of support, some are a complete joke. I would never work for either agency in my city, but I have young children of my own, so even if I wanted to, it wouldn't make financial sense.

I am extremely anti-Bill 10, but understand that some providers want the support of an agency. In that regard, I think that agency rules should have to be the same across the province, so everyone can actually make an informed decision. I also don't believe that agency providers should be allowed 6 children instead of 5, and to be able to waive the 2 under 2 rule. Just because a provider around the corner from me has wee watch come in once a month and lie about an inspection (I've seen it happen), does not make them a more capable provider than me.

I'll stop now, but to answer your question, as far a I am aware, agencies set your fees and their cut, not hours.