Let's say your spaceship can go to Jupiter in one second (Edit: as measured from Earth), which would require FTL speed. Then you turn around and come back. You've still arrived two seconds after you left.
At Jupiter, you could look through a super-telescope and see yourself still on Earth, but you still aren't really seeing yourself, because you are not still on Earth. You are just seeing the photons you passed during the trip, catching up to you.
FTL enables a kind of time travel that isn't going back in time to shake your own hand. It allows two people in two different reference frames to disagree about whether A caused B or B caused A. You don't get to go "back in time" but you can send somebody lottery results before they're drawn (from somebody's perspective).
That is exactly what it is. You should read the links above to understand what's being claimed.
Now... Please explain to me how communicating through time will allow you to literally, physically, shake your own hand as was claimed.
If I got in a faster than light spaceship and traveled to Jupiter, and then turned around and came right back, I would arrive before I left and could shake my own hand on the launchpad.
If we think humans will soon figure out FTL, it makes one wonder why we've not yet seen any human FTL spaceships from the future.