You have those problems mostly because your Tobii is external device much more far away - you won't get good enough accuracy comparing to any eye tracking that is just a camera few cm far away from your eyes.
With Apple solution (or any VR with eye tracking):
1. You have very accurate head 6d location (gyroscope, compass, accelerometer + lidar for translation) at 100+ fps minimum and very computationally cheaply without much latency
2. Cameras pointing at each eye from distance of few centimeters. In this situation Eye region of interest occupy full image resolution. Probably even VGA resolution (or less) is enough to have very accurate precision in this case
3. Because headset covers your face you don't have any problem with different lightning condition, cluttered background, whats more they use IR floodlight to have consistent lighting of pupils
4. Possibly they even use similar Truedepth IR dot pattern to get 3d depthmap of your pupils similar like truedepth sensor works with difference that here they can put thos camera more far away and have it more accurate disparity map
5. Who knows maybe they even use lidar instead of truedepth for even lower latency
6. Because sensors are so close they can have very accurate reconstruction of your eyes and distance between them - most people don't have completely symmetric eye/face
Tobii is a sensor that is just like 0.5m far away from your face. Has to track your head, estimate orientation and distance, and detected eye ROI will be a tiny crop of their image sensor even if they camera has 4K resolution (which I doubt they use such resolution). At that distance if you want to get accuracy of 1 cm of what you are looking at screen you need to detect pupil movement of ~1 degree angle. If you want even better accuracy without gitter like 1mm then you need to detect movement of pupils of 0.1 degree angle.