Aztlan, assuming it refers to a real place, would still be within modern Mexico. I'd recommend this post by /u/Mictlantecuhtli for more information about where Aztlan might actually be.

As for a link between the Aztecs and Mississippians, there are hypotheses but not particularly good ones and none that hold up when tested against the available evidence. In the latter half of the 19th Century and even into the early 20th Century, a Mesoamerican-Mississippian connection was actually the dominant theory (though "Mississippian" is anachronistic here, since that term wouldn't be adopted until later). The idea that these two cultural areas were closely linked is how we have places like Toltec Mounds in Arkansas and the Aztalan Site in Wisconsin - the archaeologists of the day named those sites in such a way to emphasize a supposed Mesoamerican connection.

In the 1930s, there's a flurry of New Deal era archaeological projects throughout the South, which greatly fleshed out our understanding of the Mississippians (and led to the invention of that term to distinguish this suite of related cultures). This new understanding also gave us the Southern Death Cult theory, which has since been re-evaluated as the the Southeastern Ceremonial Complex (SECC).

SECC emphasizes the development of Mississippian cultural features out of pre-existing elements in the area, going back to the Hopewell and earlier. The development of Mississippian societies can be traced through long-term local changes rather than the sudden introduction of Mesoamerican culture to the area. Even Mesoamerican crops, which do become widely adopted in eastern North America during the Mississippian era, don't appear to have arrived directly from Mesoamerica. Instead it seems they spread largely west to east (rather than south to north), coming from the American Southwest which had had these crops for much longer.

Additionally, there's been exactly one artifact from a Mississippian site that has direct ties to Mesoamerica. It's an obsidian scraper found at Spiro, a Caddo Mississippian site in eastern Oklahoma, the very western fringe of the Mississippi world. Like maize and beans, it probably came indirectly through the Southwest, which has stronger cultural and economic ties with Mesoamerica. As far as I know, no definitely Mississippian artifacts have been found in Mesoamerica. The closest we've got at the moment are some shells found in Mexico City that may have come from Florida or, more likely, the Caribbean. The Calusa of southern Florida apparently had gold - which isn't found in the area - in the 1500s, but we also know they were salvaging from the wrecks of Spanish ships at the time and it seems they were re-working materials taken from those ships for their own purposes. If any of those Calusa gold artifacts turned out to be genuinely pre-Columbian, they may have come from the Caribbean, or perhaps through Maya traders who seem to have had trade relations with people in the Caribbean (Caribbean artifacts show up at Maya sites and Maya artifacts have show up as far east as Antigua).

This isn't to say that idea of contact between Mississippians and Mesoamericans is completely dead. Timothy Pauketat, one of the main authorities on Cahokia, has proposed that some Cahokians may have journeyed to Mesoamerica and back again, but that's nearly impossible to prove. Additionally, in the early 1700s the Natchez in southern Mississippi seem to have had their own historical account of the fall of the Aztecs to the Spanish though their account makes it fairly clear that they were getting their information second-hand (perhaps even from the Spanish themselves before the French arrived and wrote it down). Regardless, the idea of a mass migration from one region to the other in recent history, as would be expected if Aztlan was actually within the Mississippian region, is unlikely and unsupported by any evidence.