The key to this transition, as with most transitions, is the positioning and movement of the body’s center of balance. Generally, when popping into an inverted axis, it is beneficial to allow yourself to be pulled through and out of the transition by your momentum. The idea here being that you are simply controlling and directing your energy into the flip, like a bouncing ball or skipping stone. This tends to be relatively intuitive for most people, whether than can actually achieve it or not.
When transitioning from invert to vert however, this idea of allowing yourself to continue traveling, and riding the momentum linearly tends to cause a lot of balance issues because it can initiate a degree of flip, or off-axis tilt. Because of this, many proficient kickers tend to set up their pop kicks in a very controlled manner, allowing them to easily block all of their momentum straight up, creating a tight, balanced, and somewhat stationary spin. In order to achieve this, it’s important to focus on the direction the shoulders are thrown. They must go up, and even resist the pull they’re feeling, so they rise, but dont pull the hips with them into a flip.