That is correct - a lot of people in BC start traveling after October 1st to make the most of their 6 months in the sunny south. Even though proper winter tires are required on BC mountain roads after Oct 1st the highways people do not enforce it unless snow is actually on the ground at that time. You will get at most a warning.
http://globalnews.ca/news/2256297/how-are-the-rcmp-enforcing-mandatory-winter-tire-rules/
Your situation is different in that you plan to be here during the snowy periods so you'll need proper tires.