Can you draw the spacetime diagrams that will help it make sense? I don't see how it can help because as I pointed out significant events in one frame may not be significant in another frame.
I will do that.
This event at (x=0, t=5) in the original reference frame seems significant to the nonmoving twin, why? Because that is the time he will (later) figure out that the traveling twin turned around. He doesn't see the inbound twin turn around at that time. He won't see the inbound twin turn around until much later, because of the speed of light delay.
Now, I have this temptation to say we should only worry only about "significant" events, events that the traveling twin actually observes. That temptation is probably pretty valid.
But what are those events that the traveling twin is going to observe? Well, if he's interested at all in figuring out Special Relativity, he's going to aim a telescope at Earth and observe EVERY event. He's going to be watching where he came from the whole time. So he WILL eventually see that event at (x=0,t=5), but when and where?
So he's not going to be just asking what his own watch says. He's going too be asking "What news from Earth? How far away am I from Earth?" And this question has a very INTERESTING answer (to me anyway). But you wouldn't know it by reading any of the texts on special and general relativity.