Following the de Soto entrada in the late 1530s and early 1540s, there was a period of social disruption and reorganization in the Southeast. The failure of de Soto and others to colonize the region means there's little in the way of written records following de Soto's expedition until the 1600s for the interior. In the intervening time, the Mississippian-style hierarchy had largely broken down, though some polities on the periphery--Cofitachequi and the Natchez, for example--kept it going until the 1700s. Autonomous villages and towns, bound in loose alliances, replaced the old Mississippian polities of tiered communities paying tribute to a paramount. These included coastal polities such as the Yamasee (which developed in the wake of the Guale Rebellion against the Spanish missions in Georgia) and Piedmont polities like the Catawba (which developed out of various Siouan-speaking communities that had once been subjects of Cofitachequi), but those in the interior are the most famous because they eventually became the most powerful.

The Chickasaw are almost certainly the descendants of de Soto's Chicaza. The Choctaw count Tuskalossa, who mounted the strongest resistance to de Soto, as one of their own. De Soto's Chalaque are in the right place at the right time to be the ancestors of the Cherokee, but that's less certain. Unlike those three, the Creeks were not a single people but an amalgam of various post-Mississippian peoples. While the Chickasaw, Choctaw, and Cherokee nations each have their own language with some local variation, the Creek Confederacy was truly multi-lingual from its creation. Mvskoke dominated during the early colonial period, but many other languages were spoken in the various Creek communities, including Alibamu, Koasati, Hitchiti, and Yuchi. The Creeks also absorbed members from the Yamasee eventually and, for a time, some Shawnee.

These four nations expanded their influence and power through alliances with each other and European nations, often at the expense of other nations--among them other formerly Mississippian peoples such as the Tunica, the Natchez, and the Apalachee.

Mapping the Mississippian Shatter Zone is a great source that focuses on this specific topic. I highly recommend it if you'd like to know more.