So there are two types of FATEs, the first one is after the bar fills up, this happens on single phases, such as the Mattock Phase 1, The Mattock Phase 2, these go 30 minutes after the bar is completely filled up.
Then there are First and last shift FATEs, such as the Mattock phase 3 first shift, and the mattock phase 3 last shift. The first shift happens like all other phases once the bar is complete 30 minutes after the FATE goes, then for the last phase FATE it's just 8 hours AFTER the first phase ends, there is no extra bar filling required.

I believe the timer was actually lowered for complete phases and first shift phases from the first set of Ishgard, from 3 hours to 30 minutes, due to the fact that 3 hours would cause people to go afk in the firmament and cause massive congestion.

As for progress, I dont really like how it's the same across every server, I would prefer to see some scaling now that servers are completely dependent on themselves for progress. (I dont think it's fair that lower pop servers have to work 3x more than higher pop servers and congested servers, makes the already tedious grind even more so)