Arguing with Confederates on this hellscape of a site had me digging back into the Slave state's articles of secession to find the juicy nuggets. Let's go state by state in order of secession and read them.
December 1860, a month after Lincoln wins the Presidential election, South Carolina becomes the first to vote to secede from the Union. They mention the inauguration, the Republican party, and a "war on slavery." Nothing about tariffs.
Early January 1861, Mississippi becomes the second state to secede. I think the highlighted parts speak for themselves.
A couple days later, Florida votes to leave the Union. The state secession document is very vanilla and doesn't mention reasons to leave. But John McGehee, the President of the Florida Secession Congress, puts it pretty succinctly.
Alabama (Roll Tide) becomes the fourth state to secede in January 1861. They call out Lincoln, Hamlin, and Republicans by name as being "avowedly hostile" to certain institutions. I'm sure you know what those are. Still no tariffs.
Georgia secedes next in mid January 1861. Again, they call out Republicans and Lincoln as threats to their property (slaves), their civilization, and their wives and children. No mention of tariffs or the Corwin Amendment. Just slavery.
Louisiana is next on the list of seceding states. Again, their secession document is pretty plain but Governor Moore's inaugural address in 1860 gives a taste of the sentiment at the time. Attacks on the Republican party and defense of slavery. Seems like a theme.
The last of the Deep South states to secede prior to Fort Sumter is Texas. Everything is bigger in Texas, including the attacks on Republicans for demanding abolition. They also call abolition a "doctrine at war with nature." No mention of state's rights.
Seceding states spent the next couple months sending secession commissioners to the other slave states entreating them to leave the Union and join the slaveholding republic of the CSA. It would be April and take Lincoln's call for troops to finally convince them.