Thank you TakeruK for the extremely thoughtful response!
I did apply to McGill as well but I haven't heard back from them yet. I applied to their medical physics program, for which they specifically state that a supervisor should not be selected until the second year (hence no funding for the first year!).
As for the school in my original post, you are correct, the admission went through much faster since I had a supervisor picked out who was willing to work with me. I believe that is definitely the reason I was accepted only 2 weeks after the admission deadline. I feel really lucky that I got a good response from the first prof I contacted back in the fall, and my first choice to work with. Unless things are a catastrophe at the visit or they rescind the offer for some reason, I intend to go here. So excited!
I heard back from admissions today and they have extended my deadline by 2 weeks, so things seem to have resolved themselves. I'm sure many of you can relate to that paranoid feeling I had when they didn't respond within a few days! I want to thank everyone who told me I did the right thing or gave me advice, I'm new to these forums, but it seems like an awesome community here!