Is the young Japanese man Coach Shinji? ;-)
Yes it is the foot opposite to the spearing hand that kicks. The concept is that as the spearing hand goes in, the body rotates onto the side of the spearing hand, which adds momentum and drive to the stroke. By kicking on the other side, you add more authority to the body rotation, which adds more momentum to the spear.
If you kick on the same side of the spear, you may inhibit extra authority to the hip/body rotation because your kick could be removing the maximum potential of the hip rotation as it slows hip rotation with the kick.