The congressional record indicates otherwise in very clear terms. The following is an excerpt from a speech against the tariff by Virginia Senator Robert Hunter during the secession period. The speech, which took up seven pages of the record, focused entirely on the Morrill tariff and the south's grievances against it.
"But pass this bill, and you send a blight over that land [Virginia]; the tide of emigration will commence - I fear to flow outward - once more, and we shall begin to decline and retrograde instead of advancing, as I had fondly hoped we should do. And what I say of my own State I may justly say of the other southern States. But, sir, I do not press that view of the subject. I know that here [in Congress] we are too weak to resist or to defend ourselves; those who sympathize with our wrongs are too weak to help us; those who are strong enough to help us do not sympathize with our wrongs, or whatever we may suffer under it. No, sir this bill will pass. And let it pass into the statute-book; let it pass into history, that we may know how it is that the South has been dealt with when New England and Pennsylvania held the power to deal with her interests." - Senator Hunter (page 905)
Slavery and other issues, though they appeared elsewhere during the secession debates, were absent from the speech and many others on the tariff issue.
The congressional record indicates otherwise in very clear terms.
You don't need to rehash a long winded speech from a two-bit southern politician, when you have an excellent primary source like the Georgia Statement of Secession. Here is another excerpt from it, and once again, slavery not tariffs is described as a Cause.
The feeling of anti-slavery, which it was well known was very general among the people of the North, had been long dormant or passive; it needed only a question to arouse it into aggressive activity. This question was before us. We had acquired a large territory by successful war with Mexico; Congress had to govern it; how, in relation to slavery, was the question then demanding solution. This state of facts gave form and shape to the anti-slavery sentiment throughout the North and the conflict began. Northern anti-slavery men of all parties asserted the right to exclude slavery from the territory by Congressional legislation and demanded the prompt and efficient exercise of this power to that end.
ref: Georgia Statement of Secession, January 29, 1861
The Georgia secession statement is an excellent example of 19th century white supremist demogogery. Have you even read it? Georgia Secession