Couple things here, just because I think you guys actually want to know the true facts.
Procession wouldn't be involved here. It changes the direction the pole points, but not how much it's tilted by. So it wouldn't effect seasons. A motion called nutation might have an effect, but is so minor it's not worth considering (on Earth it's only a matter of arcseconds, thousandths of a degree, in size). Procession is what causes the seasons to go out of whack compared to the calendar months and famously why the zodiac is a month off from what newspaper horoscopes claim, but there still would be seasons of the same length as always, just that maybe winter eventually starts in March instead of December if we didn't add leap seconds all the time to counteract it (and don't get me started about the differences between tropical/sidereal/anomalistic/heliacal/Julian/Gregorian/etc years, no one wants to go there...). This is turning into a really long way to say procession won't give us that effect. Moving on!
Um... Well... that would be a way to get rid of seasons I suppose, technically. But it wouldn't be pleasant and is 100% not what's happening on Eorzea. Such a world would have no apparent rotation of the sky. One half would be perpetual day and the other perpetual night, all year long. The day-side would be a scorching wasteland with the sun always hanging overhead never moving, and the night one a frozen wasteland with no source of heat. Also because this situation is the end result of tidal forces, it either takes a ridiculously long time to happen, or the planet is wayyyy to close to its star to be habitable. Not a pretty place to live, and definitely not Hydælyn.
If it does have an axial tilt though, that gives rise to seasons across the whole planet, you can't really do it selectively for regions. You either have 'em or you don't. But their impact is less noticeable near the equator where instead of spring/summer/fall/winter you get just wet/dry (and also ties in with keeping a constant 12 hour day/nighttime). Which I think is what you're getting at for maybe Eorzea could be locally season-locked. But that would be directly at odds with all our previous evidence showing Eorzea in the northern hemisphere and not on the equator. I'm gonna stick with it's just too bothersome to program and we'll never know unless the devs say otherwise. :P
When able to, I'll try and do some serious Eorzean stargazing to see if I can't give us a good numerical estimate of the latitude, since that should be possible.
Also HELL YEAH Eorzean Astronomical Society!!! I feel motivated to make us a logo now... brb