From what I understood is that its not the question of manipulating time. Its the fact that Yui must die when she reaches 20. Yui was dying when she was a kid and the mirror world extended her life till she reaches 20. So what Kenzaki was doing is to find a sacrifice to offer to the mirror world to spare Yui. So its not a question of time, Its that he can't skip the fact that she must be 20 one day. So in the end Yui accepted the fact that she will die and spared all the riders' lives.