Excluding the plantation owner class and the urban residents of the few cities that the South had, the vast majority of the Southern population was made up of subsistence farmers. These farmers were largely self-sufficient. What they did not produce on their own would be locally produced items like horseshoes, plows, hand tools, firearms, tobacco, coffee. Save for coffee, those items were produced locally or manufactured domestically. High tariffs would have little effect on their lives. These farmers fought for the Confederacy due to their loyalty to their home states, not for economic benefits. The plantation owners were leaders in their communities, and it is worthy to note that the Unionist areas in the South, such as East Tennessee, were areas where there were no plantations.
It was a common practice to devote 20% to 25% of their acreage to producing cash crops for yeomen farmers. Frequent purchases were clothes, windows, agricultural equipment, etc. The cash crops raised the money to buy all the things they could not produce. A collapse in the price of cotton or in cotton sales (or tobacco or sugar or other cash crops) would hurt their income. Simultaneously, an increase in the tariff would see Northern manufacturers raise their prices so those farmers would have less income and pay higher prices for the things they wanted to buy. That was quite painful during the tariff of Abominations so they knew full well what to expect a generation later.
In addition to that, there was a general sense that their region had been pushed around and taken advantage of - not to mention constantly insulted and derided. Not surprisingly, this bred considerable resentment. Also, Southerners were overwhelmingly Jeffersonians. They believed in limited government and decentralized power. For many of them, the post office was their only contact with the federal government. They objected to the constant drive for the federal government to usurp ever more power.