Ganesh, the actual focus sensor area is larger than the square marker in the viewfinder.
Sometime ago when testing this is approximately what I determined the actual focus area to be in relation to the square marker.
So as stated already by others, if the area under the square is low contrast but there is an area just outside the square that's higher contrast, then the camera AF will select the area outside the marker. That's why real world results are difficult to use for testing.
Self testing possible calibration issues with AF need to be done carefully and meticulously. It's best to use a standerdized resolution chart. I used this ISO12233 Chart ,but there are numerous others that will suffice. Mount it on a wall and your camera on a tripod and aligned the camera to have the sensor parallel to the wall. Make sure there is sufficient illumination for the AF system.
After not being happy with the results of 2 of my 6 lenses and careful testing, I Fine Tuned them and am now satisfied with their results. But I would caution against just AF Fine Tuning as a matter of fact and only do it after careful consideration.
Hope this helps!
Edited to add:
Also being that the DOF is so thin in your examples, hand holding can be problematic. A small shift in your position forward or back (especially using AF-S) will cause the focus plane to shift from where you think it should be. That's why when testing for focus errors it's best to use a tripod.