Yes, of Deep South representatives who voted, almost all were "no".
But outside the Deep South itself, feelings were mixed.
I've been able to identify the eight Southerners you mentioned who voted for the Morrill Tariff. One was from Tennessee, four from Kentucky, two from Maryland, and one from Virginia (paired as a yes vote). So, there were actually two from the Deep South.
If you look at the background of those eight they were all either Opposition Party, Independent Republican-Democrat, or American Party. Five of the eight were officially former Whigs, one of whom was even a Whig Presidential Elector. The Whig Party (by 1860 essentially defunct) had been in favor of high tariffs. In the past, Whigs had filed a resolution in favor of impeaching President Tyler because he vetoed a high tariff bill. Kind of hard to flip those guy's votes on the Morrill Tariff, I imagine.
Hmm, the Deep South doen’t usually include Virginia, so there was then only one Representative from the Deep South who voted for the Morrill Tariff. He was Emmerson Etheridge, from a Tennessee county on the border with Kentucky.
Important to remember, FRiend, that when the old Whigs split in two, Northern Whigs became Republicans while Southern Whigs became Americans, aka "Know Nothings".
Today we mostly scorn & mock the old "Know Nothings", but in truth, they were & are our FRiends.
Consider, for example, the election of 1848, the last election won by a Whig.
Notice those Southern counties carried by Whigs (brown):
Many of the old Whigs / Americans remained loyal after 1861.
Today we see the old Whig / American / "Know-Nothing" agenda revived with great difficulty within Republicans, using the slogan "American First" and under the astonishing leadership of a candidate who could well be our next President.