Your body must remain stacked and tensed under the kettlebell through the entire movement. You must exert full-body control and prevent any leakage of tension and loss of balance, as the weight must be directed straight to the ground through your stacked bones and tensed muscles.
This is a skill that can be easily learned through practice, at least on the loaded side. But things are different for the unloaded side, especially with a heavy kettlebell. When the weight becomes committing, your focus shifts almost totally towards the loaded side and you may fail to keep proper tension on the other, from your foot, up to your grip.
The Band-Pull Press is a great drill that teaches you how to properly tense your unloaded side.
