If we consider a hypothetical scenario where instant transportation to Proxima Centauri, which is approximately 4.2 light-years away, were possible, and then an immediate return were made, it would not result in traveling back in time.
The concept you're referring to, where the travel distance is equal to the distance light would travel in a certain amount of time, is related to the time it takes for light to reach us from distant objects. It does not imply time travel in the sense of altering the flow of time or going back in time.
In this scenario, the round trip to Proxima Centauri would simply take approximately 8.4 years as measured by clocks on Earth, while time would progress normally for you during the journey. From your perspective, you would experience the passage of time just like any other traveler. However, due to the time dilation effects predicted by Einstein's theory of relativity, time for you would appear to pass slower relative to an observer on Earth. This is because you would be traveling at relativistic speeds, close to the speed of light, during the journey.
It's important to note that the concept of time dilation and its effects on space-time have been well-established in physics. However, achieving the technological capability to travel at such speeds and experience significant time dilation is currently beyond our reach.
In summary, while traveling at relativistic speeds to a distant star like Proxima Centauri would result in time dilation effects, it would not allow for backward time travel or cause any paradoxes or consequences related to altering the space-time continuum.