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.
And the scene of Derplander Echo-tripping in the original opening movie to 1.0 was into the past not the future - he Echo-travelled back into another's memories of what was then ten years into the past to the Battle of Silvertear Skies where he inadvertently encountered another adventurer party fighting a malboro, only to be carried away by a Garlean Juggernaut into the battle against Midgardsormr and the Dravanian Horde, witnessing Middy's 'death' and the destruction of the Agrius... and the release of the Primals from the aetheric seal beneath the lake. All that happened in the game's 'past' not it's future or present. Ferne confirmed that officially in this really old thread now archived in the 1.0 forum section.
So basically, the Echo does not allow it's user to glimpse the future, because that simply is not how it works - it works on breaking down the boundaries of the soul and allowing it's user to read another's memories and glimpse their past. Because the future hasn't occurred yet, no memory yet exists of it, and hence, no Echo glimpse of the future. And the 'Power of the Echo' buff in duties is simply a gameplay mechanic that actually has no story connection, it's just a gameplay gimmick with a fancy name, nothing more - to say otherwise would be the same as saying the GLA ability 'Tempered Will' tempers the player or something equally stupid.