3.4 speculation

[SaiphaeWiloh]

That's actually not correct - the Echo does not grant the user the ability to 'see the future', because it only acts on 'breaking down the barriers of the soul', namely, literally reading another person's memories Inception style. When you view the Echo, you're viewing events that have already happened to another person, experiencing those events as if you yourself had lived through them - this is what Minfilia told the player way back at the start of both 1.0 and ARR. The Echo thus does not work on viewing future events because the future has not happened yet - unless SE adds some kind of time-travel aspect to the game, this will remain an impossibility.

To play Devil's Advocate here, that's exactly why the Echo could allow for foresight though. There's a Nick Cage movie that I can't remember the name of where he's able to glimpse the future by looking at possible actions and deducing the outcome, this is also the basis of Garnet's power in Steven Universe. Basically, if the Echo allows us to glimpse into another person's soul and see past actions and memories, but the Echo manifests differently in other people, who's to say that the Echo couldn't allow someone to glimpse into another person's soul and see intent.

This could also explain why we don't have echo users flying to help us saying "If Haurchefant does X, then Y will do Z and kill them." or "Niddhogg will attack at 8 am sharp!", While they could figure that out they'd have to be using the Echo on every person, Dragon, Ascian, etc. they pass.

I forget how we got on the discussion of the Echo and Foresight, so I can't really put it into context of how it would work in the original situation that brought this conversation up (I'll edit it once I backtrack through the forum and find it), but if the Echo allows us to see another person's soul, I see no reason why it wouldn't allow us to see glimpses of what they might/are most likely to do in a particular situation.

I didn't remember the exact situation from 2.55, but after looking on the FF wiki, I see where she sent a carriage to Ul'dah with Bernhardt, which saved her brother and the WoL. Going back to my theory of the Echo allowing her to see someone's intent -- If she was in Ul'dah when the plot was being hatched, she could have glimpsed at the intent of the plot to blame it all on the WoL/Scions. If she was able to discern the plot and the intended consequences of the plot through the Echo, she could then deduce that there are going to be Scions, her brother included, that are going to need to get out of Ul'dah after everything goes down.