I'm not sure what the fire cult is doing because I haven't read up on them as much, but I have the air, earth, and water cults down. The "hidden" locations (Riverguard Keep, Feathergale Spire, Sacred Stone Monastery) each seem to be a way for the cult to recruit and acquire materials for that cult. The Riverguard Keep group are raiding boats on the Dassarin river for goods to supply the cult. The Feathergale Societiy are wealthy Waterdavians that are probably self funded, but looking to recruit more wealthy elites. The monks in the Sacred Stone Monastery seem to sell beer, research knowledge, and transcribe documents. In addition the monks have slaves mining for something.
The Riverguard Keep seems to employ a lot of mercenaries. Jolly, seems to be with the cult for personal power and wealth with no greater ambitions. The Feathergale Society has a motivation to overthrow the leadership of Waterdeep. They can see that Yan-C-Bin can supply them with the power or skills to do that. The monks in the Sacred Stone Monastery seem to be isolationist, but they have beer and a library. I'm assuming they are selling the beer and using the library to generate an income or trade for goods the cult needs. I don't know what they are mining for. I believe it's up to the DM to use the mining for their own purposes.
What I've read of the fire cult, they seem to be a little crazy in that they are holding a huge gathering of people for the burning man ceremony. This may be an attempt to gain more followers. I'm not sure how they are supplying food, clothing, etc. for their cultists. Maybe they are recruiting druids with the burning man ceremony.