FFIX included references to most (all?) Final Fantasy games. It was a nostalgia trip. Maybe the designers sensed the passing of an era (from the old-style FFs to the FFVIII/FFX style) and decided to give something back to the fans. They considered not releasing FFIX as one of the numbered titles because of this. I don't think it's possible to suggest that all FFs were in the same world purely because of FFIX. The makers were just trying to give something back to the fans who had stuck with the series over all those years.

Oh, and Vivi loks like just about every other black mage ever, so maybe FFI etc. are all set in the same world. Or not.