That's mostly right, although I remember hearing somewhere that Vagrant Story isn't actually canon to Ivalice. When it was created all of the references were put in more for fun than to imply it's the same setting, which perhaps makes sense given how magic and the like work completely differently in that game. It's kind of a complicated mess since certain games (like Tactics) are more retroactively Ivalice than anything. It's...not always easy.