I love the thought experiment. However, what really makes me think is how air behaves.
Would the air from the destination get teleported back to fill the void that you left? Does the person just displace the air at the destination when they teleport?
What really gets me curious is what would happen during several quick teleports if the air is just displaced at the destination. Regardless, there would be an extreme vacuum at the starting location for a very short period of time. There was no specific time given about how long a person needs to wait between jumps, so you could leave a heck of a trail of destruction in your wake.
Some air would be displaced backwards after the teleport decreasing the volume of the void, but a void would still be there.
Would the forces be strong enough to suck the person backwards? Would the atmosphere simply collapse the void creating a bit of thunder and heat?
I can’t even fathom what happens to time. If you teleport instantly, that may imply that you are traveling faster than the speed of light. The universe implodes?