It existed in the sense that the Confederate States of America existed. A bunch of politicians unhappy about the countries government went into rebellion, coincidentally in the south, and then the fireworks began. But as a cultural concept, neither the CSA nor South Vietnam existed before their respective political rebellions aka they weren't "real countries". And after the rebellion was crushed they don't exist anymore in any real cultural/political fashion. If they won, they would have developed into real distinct countries eventually, but they never got the chance.

As far as invaders go, both sides invited so many vistors and advisors its hard to say who that is.

It's hard to say what a "real" country is in this case. The modern borders of Vietnam were only drawn in 1802 when Gia Long unified the country. Within 60 years, the French colonized Vietnam and split it into Cochinchine, Tonkin, and Annam. Then, in 1954, it was split again by the Geneva Accords into North and South.

As you can see, most of these divisions were short-lived and that idea that Vietnam was one unified country for a long period of time before being arbitrarily split by warring politicians is not correct.