You've basically entirely got it. I generally get a read that seeing into people's pasts is our unique Echo thing, though; Minfilia might've had it too, but Krile, Mikoto and Arenvald don't seem to do it.

It's always been pretty unclear as to why some people don't get the Echo, though; like, the Scions have been around for a lot of potential triggers, but haven't responded to any of them. My educated guess is that it only happens for souls that were once ancient souls, and some incalculable amount of people instead have souls that came into existence after that point and just wouldn't get them. If that's true, then a whole bunch of people that're gonna be born post-Endwalker will have the capacity for the Echo unlocked whenever they see something that invokes the memory of the Final Days.

As for why it didn't happen in somewhere like Thavnair, I dunno. Maybe it did, but things were too extreme at that point for anyone to bring it up? Or maybe it doesn't work if the events that invoke that are too real; like, your mind's too focused on not dying to connect to those latent soul-memories in a way that it's not if you just happen to see a starshower.