You mis-imagined the looping world in your head.
The loop does not suddenly teleport your player from north
to south. Well, it does so in the sense of the 2D map that is
probably going to be on the HUD.
Imagine walking on the 2D screen is a continuous smooth
motion where it is impossible to determine where one sector
begins and the other ends, since the character is constantly
at the center of the screen.
The south portion of the map is just stitched onto the north
portion, when the player continues to walk north. It will seem
like a smooth transition, as if there was no end to north.
In the case of a 3D sphere, he should begin to walk towards the
south pole by now, having crossed to the other side of the globe.
In the case of a 2D imaginary sphere, the "poles" are the center
and the north edge of the screen.
Distance between two poles has to be equal, right?
Well, in this implementation it is.
You just misplaced the "south" to the south edge of the map, which
is why it seemed to you as if the player was illogically teleported
from north to south.
If there was east "pole" and west "pole", this same conclusion will apply.
The true game world east is not at the east edge of the screen, but
at the center of the screen, while the west is at the west edge.
In fact, the placings of the virtual poles are totally arbitrary.
The game map still spans and is generated from left edge to right and
top edge to bottom. You just have to pick two points on the map
that are at equal distance from each other when measured in both
directions and use those as your poles.