You’re right that tariffs were a major factor in the lead-up to the civil war but I doubt that any southern soldier marched away to war chanting, “Lower tariffs.” States’ rights and the defense of their home states was the motivating factor for most Rebels. It was also one of the south’s greatest weaknesses as the states in the new nation bickered constantly about how much they were obligated to support the central government.
No they didn't. More likely they were chanting "D@mn these people who invaded our lands and are trying to force us to submit to their will."
People like to summarize the economic issue as "tariffs" but that is a massive oversimplification of what was happening. Southern Ship building industry was destroyed by subsidizes for Northern Ship building industry. Northern shipping was protected and subsidized by laws such as the "navigation act of 1817." Prices on imported European goods were inflated by protectionism so as to force Southerners to purchase lower quality Northern manufactured products.