Had an unexpected turn of luck with an Alexandrite drop, and thought it may work for Atma as well. Here's what happened:

I decide to do a duty roulette with my SMN. While waiting, I take my level 42 PLD to Coerthas to do some fates for XP. Well, while doing the fate that leads to Svara's Fall, the DF pops. Thinking I have limited time, I run out of the fate zone so I can switch to SMN and enter my duty.

Well, right after I switch out of PLD into SMN, the other people finish the fate. And what do I see? Catalyst Obtained! I got an Alexandrite despite not using my SMN in the fate at all.

I'm thinking maybe this would also work with Atma. As long as you're in your Zenith class when it ends, you could get an Atma drop.

If this is the case, you wouldn't have to worry about "grinding for no reward". You could use your pre-50 alt classes to do most of the fate, and gain the XP for each thing you kill on it, and just switch out before the fate ends and see if you get the drop too.