Tariffs are instituted primarily for economic protectionism. Funds raised from them are a significantly distinct and secondary function of them. There is no disputing the fact that the north advocated protectionism by tariffs, and in many cases got it.
The south on the other hand, as expressed repeatedly in pre-war editorials and by two of the four states that wrote declarations of causes for the war, was against protectionism because it ruined crop prices on the international trade.
I'm not sure how you can say that the tariff affected crop prices. For the years prior to the war the price of cotton had never been higher. If there was a tariff on imported agriculture, and I'm not aware that there was, then that would have benefited southern planters even more by keeping their prices high. And as for international trade, the south exported over 3 million bales of cotton in the year prior to the war. Tariffs would not have affected that.