On private property, including your own driveway, a gravel pad, or a fenced job site, no town permit applies to the container. That covers nearly every rental here, because lake lots and rural parcels usually have somewhere to set a container well back from the road.
Wilsonville is a small town and it does not publish a street or right-of-way rule for containers. Its published ordinances cover water and sewer rates, zoning, grass and weed abatement, unsafe structures, and a handful of tax and administrative matters. If the only workable spot for your container is a town street or shoulder, call Town Hall at 205-669-6180 before you book so the placement is agreed in advance. The office is at 9905 North Main Street.
Two other authorities can come into play. County roads outside the town limits are the county's, and a state route through the area falls to the Alabama Department of Transportation. Which one applies depends on the road your container would sit on.
One town rule does bear on larger projects. Wilsonville has its own ordinance on the remedy or demolition of unsafe structures, and zoning regulations that apply to new work, so a teardown has a town approval path even though container placement does not. Tell your account manager the exact address and the type of job, and they will help you find the right office before delivery day.