When Luca and Alberto use their white skill and Ko’s all enemies then would move on to the next wave. They would be untargetable until they cast their white skill again. It’s pretty obvious why this is happening is that when using their white skill they become untargetable. And when they finished the wave and moved on they are still considered untargetable.
On another note, I think it’s kind of annoying that their Purple skill would interrupt any of their skills. It can interrupt the White Skill, Green Skill, and Blue Skill.