The Virginia Convention, and I suspect the other state Conventions, were separate bodies from the state legislatures, elected by the people and similar in nature to the conventions used to create and rewrite state constitutions.
The timeline in VA was as follows:
January 7, 1861
Virginia calls a special session of its Assembly to consider convening a convention on the question of secession.
January 14, 1861
Virginia Assembly approves a convention to consider secession
February 4, 1861
Elections in Virginia create a pro-Union secessionist convention
February 13, 1861
In Richmond, former President John Tyler and former Virginia governor Henry Wise lead the notables who meet for the first time as Virginia’s secessionist convention.
April 3, 1861
A “test vote” in the Virginia convention shows a 2-1 margin against secession
April 4, 1861
Virginia’s secessionist convention votes 80-45 against secession.
April 17, 1861
Virgina Secession Convention approves the wording of a referendum of secession and calls for a popular vote to approve it.
April 23, 1861
Virginia secessionist convention ratifies a temporary union with the Confederacy and accepts the Southern Constitution, subject to approval of the ordnance of secession Virginia
May 23, 1861
Virginia ratifies the Secessionist Convention referendum by a vote of 132,201 to 37,451 Virginia
http://blueandgraytrail.com/event/Virginia_Secession_Convention
What you missed in that timeline was May 9, 1861, the date that Virginia was admitted to the confederacy. Had the referendum gone against secession then what? Do you suppose they would have asked to be let out? </sarcasm>