Your eyeballs are probably rotated, maybe something like this:
so that mirroring along the Y-axis doesn’t work as you would like.
If you have rotated the Sphere in Object Mode, you can fix it by pressing ALT+R to re-set the rotation and then rotate 90° around the X-axis again, but if you accidentally rotated in Edit Mode, it is probably the best to delete the eyeball and start with a new UV-Sphere.