I needed to correct him big time. After I re-established my leadership and he was soft and responsive I went for a short ride before heading out for a trail ride. When we came back I took my sister for a ride on the lunge-line, and then my brother.
Now that I write this and reflect back on the session I think I know why Kai was so testy. I remembered that right after I took him out of the paddock I let my sister lead him. She is much less confident than I am and Kai must have sensed that. I usually only let her handle Kai after I work with him but I want her to be more involved with Kai so I thought it would be ok to let her lead him. I show my leadership and confidence right from the moment Kai sees me. He usually tests me in one little way, for example by pulling back slightly. I always correct him and we continue to the arena no problem. I am now aware that Kai looks for my leadership right away and he needs me to be a leader for him from the start and that I naturally did it without even thinking about it.