During the period between 1850 and 1860 tariffs had been reduced considerably. The Morill Tariff was defeated in the Senate in 1860. So if tariffs were indeed the cause of secession, and there is nothing that suggests they were, then the timing is suspicious. Why secede over something that had been going down for years and which did not impact you very much to begin with?
The agitating for the Morrill tariff actually got under way in around 1858 or so, IIRC. The south saw higher tariffs coming, and Lincoln while campaigning for president, supported Morrill’s scheme.
The history of tariffs were just another cause of southern dissastifaction, but not the only reason to secede. Had that been the only issue, it wouldn’t have been enough, southern reps. could have fought it out in Congress.
But individual state sovereignty trumped it all, and it was states rights that tipped the scale.