Morningstar is right on all counts - although SE has been using the term 'the Echo' to describe the potent buff given if you fail a quest battle/trial/dungeon and then repeat it, it's effectively just flavour text and has no connection to the actual storyline. The Echo itself is simply a psychic ability that allows a person to view another person's memories, (rarely), understand another language that they've never learned, and also protect them from a Primal's corrupting influence.

The Echo isn't actually sending the player through time, they're basically in a dream, viewing another people's memories in a semi-waking state. Hence, because of this, they cannot view the future, because the future hasn't happened, no memory exists of the event and thus, no Echo trip to the future.