No they didn't. Why do you assume all the imported goods would have to be sold exclusively in the South? That's not how it worked. They were sold all over the place. Textiles were a really big deal. That's what powered the industrialization of Birmingham and mills up in New England were some of the larger employers of industrial workers there at the time.
Yes, I agree. The New England mills were making textiles… lots of them. And they were using Southern cotton to do it. But they weren’t paying tariffs to buy the cotton or to sell the textiles in the United States. Only imported textiles were subject to the tariff.
So what was it that those poor Southerners were getting taxed on so disproportionately that they were willing to go to war over?