Well, they didn't.
During 1860 the imports of the South were valued at $331 million; those of the North at $31 million.
http://encarta.msn.com/encyclopedia_761557415/Confederate_States_of_America.html
In summary, during that year the Port of New York took in $233.7M, of which $203.4M were subject to tariffs ranging from 4 to 30%. During that same period, all other U.S. ports combined received $128.5M in imports, of which $76.5M was subject to tariff. So the Port of New York, by itself, handled almost two-thirds (64.5%) of the value of all U.S. imports, and almost three-quarters (72.7%) of the value of all tariffed imports
Source (and hey, my link actually works)
It's very unlikely that most of those imports made their way South.