While the Unionists won, a number of Tennesseans who otherwise voted in favor of the Union were against the use of force against the other Southern states, which was viewed as "coercion." Therefore, when Lincoln called for volunteers after Ft. Sumter, the mood changed, as the call was viewed as part of coercion.
The Tennessee legislature passed a "Declaration of Independence" which said we don't take a view on the "abstract" question of secession, but invoke our ancient constitutional right to change or alter the government. See Article I, Section 1 of the Constitution of 1834 (or our current constitution). Two questions were made up for the voters, one to approve the Declaration of Independence, the other the adoption of the Confederate Constitution. Both passed by direct vote without a convention.
Sam Elliott