Your idea kinda fits though with the following ideas.

The Crystal Tower in FFIII was an attempt to manipulate time, in FFXIV we're not sure. The legends surrounding the area where it's located, Silvertear falls, are connected with Athlyk, the god of Time and Nymeia, the Goddess of Fate. The tomb of Xande was the location of Athlyk's symbol. FFIII says that Xande tried to manipulate time to avoid his fate (mortality) by creating an imbalance between light and dark, like what we saw during the Seventh Umbral era with the appearance of Atomos in the chaos.

The explosion of the Agrias at Silvertear Skies, let loose a powerful explosion that allowed, not only the primals to escape, but also, gave the ability of specific adventurers to also experience a type of time travel involuntarily. The "starshower" seen could be the rift occuring and the imbalance between light and dark beginning.

The whole story probably doesn't connect directly with FFIII of course, as we're in a different time/dimension. But I find it interesting that we have Xandes, and I wonder if Nymeia and Athlyk would correspond to Unei and Doga, both of whom seem to have been able to transcend different time and dimensions, and don't actually die. Nymeia the watcher of celestial bodies and the spinner of Fate and Althyk the space time surveyor appear in Eorzea before anyone else.

In FFIII it's Unei and Doga that cross dimensions to a land that is called Eureka, which is accessible through the Bottom of the Crystal Tower. If Eureka = Eorzea, it might explain the sudden access we have to the place after all this time.