Yes, you do. While many provincial health care plans across Canada have reciprocal billing agreements (except Quebec), certain services will be up to you to pay for when you're travelling in those provinces.
Examples of things that are excluded under some provincial plans are prescription drugs, dental care, optometric, chiropractic, and ambulance services.
Purchasing emergency travel medical insurance can provide you with coverage for such care.
See the Gov't of Canada's site for more info on this topic.