I think this represented the will of the voters, but not the (white) population.
That's a theory that you are free to advocate and defend if you like, but three issues still remain:
1. The voter turnout for the secession referendums in all three of those states is on par with their typical voter turnout statewide in a presidential election year, suggesting that the secession electorate was representative of those states' normal electorate.
2. Your book either claims or implies (I don't remember the exact wording) that no southern state held a referendum and that they all seceded through convention, does it not? If so this is in the very least a factual error.
3. Even if we were to assume your theory about the will of the population were true, do not the secession referendums also violate the quote you gave in your book purporting that the south collectively seceded on the approval of only about 600 or so power elites? Those referendums indicate that in addition to the 600 or so convention delegates the decision included roughly 385,000 members of the voting public?
Now, according to the 1860 census Texas had 228,585 white males total living there. Of this figure 109,625 were older than age 19. The categories were not recorded statistically between 19-21, but a reasonable guesstimate puts the adult white male population in 1861 is about 100,000. We also know that exactly 60,900 voters participated in the Texas secession referendum, putting statewide voter turnout at 61% of the maximum possible electorate. I think you would be hard pressed to argue that 61% turnout is unrepresentative under any circumstance. Care to reevaluate your position?
Tennessee's referendum had 151,654 participants total. That puts their turnout among the maximum potential electorate given the time (all adult white males) at 86.6%. Do you care to tell me that 86.6% is not representative either?
On to Virginia now. In the 1860 census they had 528,842 white males. Of those 246,016 were in the 20+ age range. Using another reasonable guesstimate, let's suppose about 225,000 of those were 21 or older, making our maximum potential number of voters (assuming all adult white males participated) the same. 169,652 people voted in Virginia's secession referendum. That puts turnout at 75.4%. Now tell me. Is that unrepresentative of Virginia's popular will as well?