I believe that outside of Texas none of the seceding lower south states who seceded before Fort Sumter held actual secession referenda. Instead voters were only able to choose delegates to secession convention.
I would argue that had actual secession referenda been held, at least some of the lower south states would have voted against secession, with Georgia being my most likely case. In Georgia about 50% of the voters actually voted for some type of unionist delegate anyway according to one study of the issue.
It is a strong sign of the overall weakness of the secessionists that they were afraid to actually hold referenda in these states. I believe the unionists tried to get a referenda requirement passed by the conventions and in one state (maybe Georgia or Alabama, can't remember which) came just a few votes short in the convention of getting one. In a referendum, the dispirited and divided unionists would likely have gained new strength and momentum, and a silent unionist plurality might actually have won out in many of these states. I refer to a unionist plurality in that the southern electorate was divided into many factions in early 1861, hard core unionists, marginal unionists, conditional unionists, people on the fence, and a similar split among secessionists. In a referenda setting, a unionist outcome was more likely than a convention setting.