Carbon taxes have actually been pretty extensively researched and are proven to be effective over time. There is lots of research out there if you want to dig.
I'm not sure why it should be a surprise that making a good more expensive (carbon) causes people to consume less of it. It would be far more surprising if carbon consumption worked unlike literally any other market good. Carbon behaves like literally everthing else in a market economy:
Right now, carbon is mostly subsidized and cheap.. It sits at the bottom right of that graph. Low cost, high supply, high demand. Introducing the carbon tax moves it up the demand curve by increasing costs, reducing demand. The more expensive you make it, the further to the right it goes and the less that is consumed. It's literally economics 101 and basically every market good in the history of the planet has operated on some version of this graph. The graph looks a bit different of course depending on the good and how elastic demand is, but all goods nonetheless operate on this curve in some capacity.
Like other market goods though, the market reaction will be proportionate to the scale of cost increase. Right now Canada's carbon taxes are still relatively low, despite all the hoopla they get about them. And since they are low, they offer a low amount of incentive for the market to shift demand away.
By 2030 when the Carbon Tax would be at $170/tonne (minus the fact that it will be exceedingly unlikely to last until then), the market cost on the good will actually be significant and which should start to create significant market incentives for markets to minimize exposure to those costs.
Carbon Taxes work like literally any other market incentive/disincentive provided by the government. Just like sin taxes, etc.
Like sin taxes, I suspect that conservatives don't like the carbon tax as it exposes how high-carbon many conservative's lifestyles are. Many rural residents believe city-dwellers are the "polluters" but the reality is usually the dead opposite. Economic models for ye and not for me, so to speak.