ARR's raids had us going into Allagan spaceships and parts of a fallen satellite filled with robots and the 1.0 trailer featured dragons fighting giant airships that were shooting them down with full-on 20th century machine gun fire so the anachronistic levels of technology have been here since before the original iteration of the game even launched. The infamous ARR MSQ dungeons have control rooms with giant computer screens, wrist-mounted radios, electronic jamming, and a fight with a giant robot in a sleek elevator.
The original art director for 1.0 was the same that did FFXII which also has airship dogfights with machine guns alongside knights with bows and chocoback so it's not a surprise. Anachronism has been a key aesthetic of the Final Fantasy series for decades.
I'm also not sure what your OP is about in regards to the three starter cities because most of the whole world is just as medieval as they are. The only contemporary technological societies are the Garleans and the Alexandrians and one of them has only just teleported into our world. Our nations are still adapting to sudden influx of technology from defecting Garlean engineers but we still have airships. Ul'dah has ceruleum derricks and refineries, and Limsa has guns, cannons, and ceruleum-powered pirate ships.
Everyone who isn't the Garleans doesn't need super high-tech to fight them anyway. When the average peasant can augment their strength with aether, let alone adventurers running around flinging fireballs and augmenting arrows to pierce through Garlean chestplates, technological research is going to be slow. Especially in a realm full of city-states that did not even have strong diplomatic ties with each other until 5 years ago. Technological progress requires necessity and communication and the Garleans and the Alexandrians are the real outliers here.