The Morrill Tariff of 1862 was already in the works, everyone knew what the Republicans wanted to do on tariffs -- and Morrill was the Son of the Abomination, so to speak. The Republicans were high-tariff guys, and the Southerners knew it.
According to the very first proposed declaration discussed by the Georgia secession convention, tariffs weren't the issue that caused alarm:
"The State of Georgia is attached to the Union, and desires to preserve it, if it can be done consistent with her rights and safety; but existing circumstances admonish her of danger: that danger arises from the assaults that are made upon the institution of domestic slavery, and is common to all the Southern States."
That's danger from assaults on slavery, not from Republican tariffs.
I found a link to the proceedings of that Georgia meeting and didn't see any concern with tariffs. But I admit that I wasn't looking too hard or expecting to find it. Maybe somebody can find a preoccupation with tariffs that matches the worry about slavery expressed in the above quote.
The regular Democrats had a little more moderation in their platform, but it was still dominated by slavery with a call for a railroad. No concern over tariffs expressed by the Douglas Democrats
You are right about the Republicans openly supporting tariffs, but even in their platform the subject takes a minor place compared to the slavery issue.
Here's the link where you can find all the party platforms over the years:
I just can't find a great Southern concern about tariffs in 1860 except as an after the fact justification for rebellion. Yet more evidence that from the Confederate side, the war was all about slavery.