that's not a catch, that's the whole point. It's not just a punishment for the countries that are polluting, it's also a punishment for people who externalize their pollution by buying from countries that are polluting. Putting all the responsibility on third-world countries doing the manufacturing and none on the consumers who buy whithout concern for where their products come from is the whole problem. the consumer nations should bear the burden of sustainable production just as much if not more than the producer nations.
Trump's tariffs are dumb because they ignore the impact on the consumer, but that doesn't mean tariffs are bad. A tariff on pollution means we stop externalizing that cost. If we pay the cost of pollution, it makes non-polluting alternatives economically viable.
"Your own" citizens bear the burden of higher prices from that country, but this is a desired outcome: goods that have higher externalities should cost more. That's the whole point of a carbon tax.
And unless a country really has a lock on a resource, higher tariffs ought to mean the products start being produced in the host country, which is good because it will be being made under the better carbon policies.
Tariffs are dumb when they're enacted out of spite, enacted out of some false sense of balance, or enacted as a short-term bandaid to try and prop up a failing local industry. But in the case of carbon taxes and policies, they would seem to do exactly the right thing: discourage consumption and production of carbon-heavy resources.
With carbon tariffs the entire point is to reduce import of CO2 intensive products. The only failure criteria is if people abolish the CO2 tax/tariff.
Well, a caveat: if the scofflaw country is selling you luxuries probably they suffer from the tariff. If they are the sole or chief supplier of the good/service and it is a necessary good/service, then you're just causing trouble inside your own borders: your citizens pay the cost of the tariff. Maybe you can use this revenue stream to make your economy greener, but you're still keeping the change inside your borders.