You're neither creating nor destroying any new money.

Bob is average. Bob pays $100 in carbon tax and then gets a check for $100. He doesn't have any more or less money to spend than he did before. He is able to continue his existing behavior and make no change whatsoever, if he wants.

But now he has the incentive to make a change. Because if he installs electric heat pumps instead of heating his house with oil, now he is only paying $50 in carbon tax but still gets a check for $100. If he can get the heat pumps installed for a monthly payment of less than $50, that's what he's going to do. And that's the goal.

Ok, I follow now. I do remain skeptical it would work in practice though in any meaningul way to get people to reduce their carbon footprint. For that to work, the numbers would have to be truly significant. I'm not sure what those numbers would look like, but I imagine if people cant forsee the immediate economic benefit to them in the very near future, it wouldn't work.

They would foresee an immediate economic benefit to them. Many of these technologies are already close to breakeven. The numbers above are a simplified arbitrary example. Try this one.

Bob needs a new furnace. Heat pumps are more efficient and save on energy costs, but also cost more up front than a new furnace. That basically evens out, so maybe right now the heat pumps still cost $5/month more than the furnace, at least in the short term. Until the cost of operating the furnace goes up $50/month because of the carbon tax, in which case he wants to immediately save $45/month.

And Bob is average. Alice is a heavy user. She has a big old house that she likes to keep at 90 degrees all winter, so the carbon tax would increase her heating bill by $500/month, which she can save by switching to heat pumps and installing solar panels on her roof. So she's going to do that right away.