I wanted to test and provide better more accurate information on this before i posted it but, with finals and what not i don't quite have the time. So on that note there is a theory that the atma are more available in areas at certain times.
This is a reddit article talking about it. I hope it helps us out on cutting back on the time needed to farm. Good luck and happy hunting.
http://www.reddit.com/r/ffxiv/comments/22p1w8/japanese_atma_farming_theory/

I have tested this out.
I'm not 100% sure if it does work, or it's merely just a coincidence.
I tried this a few days ago, got 4 ATMA Crystals within the hour.
While the ones I didn't took a lot longer. (East Shroud 8 hours of farming)
Some worked immediately (5 -10 Fates)
While others took a lot longer
(Got one of them at 7:59,and started at 7:00 exactly)

So I wouldn't say this is a guaranteed way to get an ATMA, but it really does increase the likely hood of the drop at best.

Anywho, Happy ATMA farming