I'm not a fan of the multiverse theory, because thinking rationally, since there hasn't been a consistent hand at the wheel since 2001, there's no way all these teams were thinking about anything beyond the current work. Some writers like Nojima feel differently, and try to link their worlds together (see the X-2->VII retcon), but those should be considered exceptions, and not the rule.

I think it's better to think of it as each game has its own multiverse containing the other games' worlds in some form, but those multiverses do not connect with each other. You have to consider the lore of the source game as well as XIV to determine the validity of the connection. For example, while it may be tempting to think of the fallen thirteenth shard as "the FFIII world" because of the Cloud of Darkness, her presence there in a different form of existence than she had in FFIII is what actually rules out the possibility of a direct link.