Honda City is equipped with the improved CVT. So far, it is very
smooth going, with no jerk whatever, as with the problems you have
described. Even with urgent need for speed and you depressed the
pedal hard, you can feel the car picking up speed fast without any
jerk.
I have sat in my friend's Vios which is equipped with so called
super auto but I felt a slight jerk with each gear change, even
though I am sitting in the rear. His car only 2 months old.