So the fifth person to arrive moves to the centre of the tetrahedron and shifts roughly 1.299m into the past or future.

I have a few questions.

1. How do you attain time offset?
2. Doesn't that make conversation difficult?
3. What even is the fifth dimension?
4. How do you convert a distance in metres into a distance in time? You would surely then have a universal m/s? Oh, wait, there is a universal speed, it's the speed of light, which means 1.299m is equivalent to about 4.3 billionths of a second, which is considerably less impressive for question 1 and just not at all problematic for question 2.
5. If you're using very fast motion for your time offset, doesn't that make conversation even more difficult? How fast would you need to be going to dilate time for a few billionths of a second? Doesn't Heisenberg uncertainty start to have an impact here? How can you be sure you got it right?