The article is interesting and would I enjoy reading other like it. However, the issue of secession has nothing to do with how a citizen voted in 1860. Men who voted for the Breckinridge - Lane ticket wanted them to lead the United States, not lead a secession movement.
To return to the point of the article - how did Southern counties vote based on number of slaveholders -- two counties in Alabama may serve as illustrations. First, Bell-Everett carried Macon County in the Black Belt region. The ticket ran a strong second in most Black Belt counties. If I'm not mistaken, Bell also won in Pickens County AL.
On the opposite side of the coin, Winston County AL ranked among the lowest for slaves residents in 1860. Breckinridge easily carried Winston County. You will quickly recognize its significance in the Civil War as the "Free State of Winston". The Breckinridge - Lane ticket also did well in so-called 'Avalanche Counties", districts where Democrats normally attained large majorities.
What does this mean? Voters (and in this day all voters were adult white males) don't normally break from established patterns, at least not in large numbers. The Bell-Everett ticket represented itself as one that should be supported by all those wanting the Constitution to be respected, the laws of the United States to be obeyed, and regional animosities to be set aside in favor of the common good. In reality the supporters of the Consitutional-Union party were former Whigs.
Whigs favored internal improvements (bridges railroads and canals), public education, a national bank and a strong central government. Party leaders included Henry Clay, Daniel Webster and Zachary Taylor, among many other familiar names. A true Whig despised the mention of President Andrew Jackson.
Northern Whigs opposed the expansion of slavery but favored a high tariff to support internal improvements. Southern Whigs were in oppostion to both points. Eventually Whigs adopted a compromise tariff not to exceed twenty percent, which most could support. However, Whigs split on the Kansas-Nebraska Act of 1854, and the party ceased to exist.
In the mid-1850s Northern Whigs helped organize the Republican Party, while others (especially in the South) joined the short-lived American Party, AKA "Know-Nothings".
No matter what the politicians called themselves, voters knew them for what they really were. For example, Abraham Lincoln was a self-described "old-line Henry Clay Whig". Here's a paragraph on Mississippi Whigs from Southern Historical Quarterly, vol. 29, no. 3, "Mississippi Whigs and the Annexation of Texas", by James E. Winston.
Historians of the Whig party in the South have pointed out the interesting fact that it was recruited mainly from the aristocratic element of the black belt. This was eminently true of the party in Mississippi, where its chief strength was drawn from the rich planting interests of the fertile river bottoms. The Democratic journals were ever referring to the broadcloth gentlemen, to the rich nabobs of Adams and Wilkinson Counties, where the larger cotton planters resided, and where solid Whig majorities could always be counted upon. According to the Natchez Free Trader, ever a determined opponent of Whiggery, the members of this party were conspicuous for their wealth and talent; the party seized upon cities and towns, thus obtaining control of the financial institutions, and recruiting its strength from the banks, lawyers, doctors and parsons. Many a Democrat being in financial difficulties, had grown lukewarm in his allegiance as a result of the sinister influence exerted by the capitalistic elements of his community. "We have Democratic lawyers fully as eloquent, doctors equally good at curing or converting, and Democratic parsons in abundance; but somehow or another they will not preach politics."
To return to the original point people who supported Bell-Everett in 1860 were former Whigs, and former Whigs supported the interests of planters, bankers and businessmen. They would be out of place and in terribly short supply in predominantly rural Southern counties. That's why Bell did so poorly outside the larger towns and the Black Belt counties.