I'm assuming that the South is an independent country in your scenario? So again, why would goods destined for Northern consumers go there? The tariff makes no difference to European supplier because they don't pay it, the consumer does. Goods that U.S. consumers want will have to cross the border at some point and the U.S. tariff would be applied there. If the Confederacy has already applied their own tariff then that would serve to make goods shipped via the South to be even more expensive. As for Northern goods meant for Southern consumers those would be taxed at the same rate as European goods would be so the European goods would not have a cost advantage.
Goods bound for the American market as a whole could have gone to any port when tariffs were equal. Lower tariffs would draw off trade. This had been illustrated for years in New Orleans where the Baratarians ran a thriving smuggling business. The long border between a coastal Confederacy and its US neighbors would have been hard to police.