There are a lot of misunderstandings about general relativity, but it is indeed so that it would be theoretically possible for you to travel from Earth to Alpha Centauri in one second (assuming you could somehow withstand the acceleration), and then come back in one second, from your own point of view. The problem would be that over 8 years would have passed on Earth (for an observer on Earth you would have never surpassed the speed of light at any point, and your travel would, from this perspective, have lasted over 8 years.) Cool way to travel to the future, but not very practical to organize events.
However, in science fiction the idea of creating a wormhole is that, at least theoretically, a shortcut is created by bending spacetime. In other words, you are not actually traveling that 4 LY distance from Earth to Alpha Centauri, but you are literally and physically traveling a significantly shorter distance, a shortcut created by bending spacetime. It's like burrowing through the Earth in order to not have to go around it in order to get to the other side (except in a much more extreme form in this case). This would mean that you are traveling significantly less than 4 LY, and thus time dilation is likewise significantly less (although it would still not be zero).
Theoretically the GR spacetime geometry would allow that, but there might be no way to actually do that in reality (at least not that fast). But in science fiction we can speculate what it would be like if it were possible.