well, demonyms in a southern victory timeline could go in many directions. in my opinion, one likley option is a smewhat complicated system where citizens of both countries claim to be "american", while refering to each other depending on the situation as either "federal" and "confederate" or "yankee/yank" and "rebel/reb". the rest of the world would probably end up calling them "u.s." and "c.s."
of course, "dixie(an)" does sound pretty cool, especially if paired with "usonian" for northerners.
I'd imagine that the terms would be:
"American" - in national use (when referring to one's self)
"Unioners or Northerners" - US citizens as referred to by CS citizens and possibly the wider world in polite fashion
"Confederates or Southerners" - CS citizens referred to by US citizens and the wider world in polite fashion
"Union Americans" - US citizens as referred to by the wider world (and possibly CS citizens) in the most polite context
"Confederate Americans" - CS citizens as referred to by the wider world (and possibly US citizens) in the most polite manner
"Yankees or Yanks" - US citizens in a more slang (and derogatory?) fashion
"Rebels, Rebs, Dixies" - CS citizens in a more slang (and derogatory) manner.
"Gringos" - US and CS citizens in a slang and derogatory manner by Latin Americans.