No, they seceded after the north stopped respecting slavery, when "an increasing hostility on the part of the non-slaveholding States to the institution of slavery, has led to a disregard of their obligations, and the laws of the General Government have ceased to effect the objects of the Constitution. The States of Maine, New Hampshire, Vermont, Massachusetts, Connecticut, Rhode Island, New York, Pennsylvania, Illinois, Indiana, Michigan, Wisconsin and Iowa, have enacted laws which either nullify the Acts of Congress or render useless any attempt to execute them. In many of these States the fugitive is discharged from service or labor claimed, and in none of them has the State Government complied with the stipulation made in the Constitution. The State of New Jersey, at an early day, passed a law in conformity with her constitutional obligation; but the current of anti-slavery feeling has led her more recently to enact laws which render inoperative the remedies provided by her own law and by the laws of Congress. In the State of New York even the right of transit for a slave has been denied by her tribunals; and the States of Ohio and Iowa have refused to surrender to justice fugitives charged with murder, and with inciting servile insurrection in the State of Virginia. Thus the constituted compact has been deliberately broken and disregarded by the non-slaveholding States, and the consequence follows that South Carolina is released from her obligation."

They call out Lincoln's inauguration and his perceived attitude on slavery, not tarrifs:

"On the 4th day of March next, this party will take possession of the Government. It has announced that the South shall be excluded from the common territory, that the judicial tribunals shall be made sectional, and that a war must be waged against slavery until it shall cease throughout the United States. "

https://avalon.law.yale.edu/19th_century/csa_scarsec.asp