Yep, you are true here!
For scheduled stuff, there is a precision for things to happen in Eorzea. But that doesn't mean they will stick to the same precision when talking about specific dates of events. Day x, month y, year z for every event. It's more like "in the year z..." or "it's now almost z years since..." Maybe, in some old books we can see more precision in this. Like the Aetherostronomic thing the Ishgardians have at Coerthas. maybe there, all things are very very precise! But, out of there, not so much...
All what I meant was: eaorzean people are not controled by the clock (like we are in real life). Beside all the use of clocks for scheduled stuff (like transportations, ships, GATES, etc), for the regular track for especific dates of events, they use aproximated times, not a very precise one. That's all that I've said. I never said they don't use clocks, just not that often for everything in their lives (like we do irl).
They have a calendar, yep. But they not stick to it for every single thing (as we do in real life). The precision of time is like a "new stuff" for them like if they are living in a transition or a mix of cultures. The garleans, on the other hand, seems to use this precision more often, more daily. Maybe because they lack the connection with the aether and need to control more their own time using transportations to be a more efficient society.
In a way, the use of the clock is like real life transition: as we relate more to technological progress we depend more on the control of our time. And when we don't need that much technology, we could stick to a more wider view of the passage of time, marking "the older days" of our culture since progress is related to technological evolutions. Eorzea seems to be in between moments having some advances, but a culture not so related to the precision of their passage of time... yet.
They have track of their time in a daily basis, sure. But this track is not as precise as the garlean ones for historical events outside their books.