I'm not sure that it makes a difference whether you do FATEs or CEs for the purposes of Atma farming.

Every single Atma I currently have I got from a FATE. I've gotten zero atmas from CEs.

My friend who I've been doing this with since the start has zero atmas currently. We've done every FATE and CE together. Except for when I had to go AFK once, he went to a CE without me. I did a FATE waiting for him. I got an atma from the FATE, he got nothing from the CE.