John: I cannot speak in general terms about all Alabama regiments, but I have some information about how the 14th Alabama was formed. Most of the companies that eventually became companies of the 14th Alabama formed first as individual companies in their home counties in early July 1861. The Regiment was officially formed by Special Order Number 110, dated July 30, 1861, from the Adjutant and Inspector-General’s Office, Richmond, Virginia. (Paragraph VII). (You may want to research orders at the National Archives from around the time the 9th Alabama was formed to see if similar orders exist for the 9th Alabama.) Two of the companies that were designated as companies of the 14th Alabama in this order did not join the regiment when they gathered at Camp Johnston, near Auburn, Alabama at the end of July 1861. Those two companies that did not join the Regiment were subsequently replaced by two other companies from different counties. (The two companies that did not join the 14th Alabama were eventually assigned to other regiments.) Marshall B. Hurst, the historian of the 14th Alabama, who served with the Regiment wrote in his history that the Regiment rendezvoused at Auburn on August 1, 1861 and the regiment was mustered into Confederate service on August 7, 1861 at Camp Johnston, near Auburn, Alabama.
So to answer your question directly. . . for the 14th Alabama, the companies were first raised and organized. Then they were assigned to the regiment. The two companies that replaced the companies that did not join the regiment were also raised before they were assigned to the regiment.