So I was very confused as to why one of my gates was putting me to the left of the destination gate when travelling, and going the other way around required me to execute random maneuvers while inside the origin gate.

After a couple of hours of confusion and experimentation, I noticed that the exit position (and apparently the detection to teleport when entering a gate) are related to the grid's pivot point.

So just make sure that your pivot point is correctly oriented and, as far as I can tell, as close to the center of your ship as possible!! No more weird exit points, no more having to dance inside the gate.

Hope this helps someone else :-)