During World War II, many people started to migrate to the South and the West because jobs were opening up and new jobs were being created.
A lot of new industries were being created in the South and West during World War II. Thanks to defense spending, ships and aircrafts were being created both in the South and in the West. Things like ships and aircrafts were needed in World War II and they needed a lot of them, so the only way to get as many as they needed was by opening up numerous industries around the country.
While the West had created more industries than the South did, people were still migrating to both. The South did not have as many cities as the North or the West did, so they simply did not have as many industries. Even so, since new jobs and opportunities were opening up, people still moved there in hopes of getting a job.