obviously the call for troops was not the primary reason for the first seven states to secede and they certainly seceded over the slavery issue.
The same is obviously true for Virginia, Arkansas, North Carolina, and Tennessee. The thing is states are not people. There were plenty of fire eaters in all of those states who were ready to secede early. The only real difference between the upper South and the lower South was in the number of conditional unionists—many of whom were ready to secede over slavery but needed a bit more of a nudge.
It is not "obviously true" for the Upper South. They seceded when Linocln called for 75,000 volunteers. Even after Lincoln's call there were still slave owners in those states that did not want to secede. Not every slave owner was a fire eater and not every fire eater was a slave owner.