So, I just started the first book after getting my Atma weapon and I found that one FATE in particular was taking a long time to pop:

Giant Seps

After doing some searches on the web it seemed that people had reported anywhere from 90 minutes to 6 hours or so on the spawn time... of course leading to a ton of complaints. Some even suggested that the FATE would pop by killing the dragonflies near the spawn point.

I got bored while waiting and killed a few dragonflies. Nothing happened. Waited some more... killed the one right next to the entrance to The Stone Vigil and Seps spawned IMMEDIATELY after!

Bam, FATE done

Now, off to Outer La Noscea to kill some Synthetic Doblyns and find the FATE "Make it Rain". I see a bunch of plasmoids around the spot where the FATE pops and I figure... let's see what happens?

I killed a single plasmoid and the FATE popped!

So, instead of waiting around for a FATE that seems to take a long time to pop... do yourself a favor and kill something