Six states leaving after Lincoln's call for troops were Arkansas, North Carolina, Virginia, Tennessee, Kentucky and Missouri.
Minor error -- North Carolina left the union on May 20, 1861. If I'm not mistaken, Lincoln had taken his oath of office some time earlier.
"Arkansans appear to have been positioning themselves for secession well before Lincoln's request for militia."
Most of the earlier votes against secession opposed immediate severance of ties with the union rather than supporting union under any conditions. The voters simply determined to await developments, which finally came in the form of Lincoln's call for troops.