It is about when they are or aren't in the light cones. If we remove relativity for a moment and define some time T=0, then Alice and Bob do see different things. The thing is that at 0, Bob and Alice aren't in each other light cones. Future Bob is in Alice's light cone and future Alice is in Bob's light cone, but at current they aren't. So you in the case of Alice, it is a question of what is in Bob's light cone.

There is also the matter of possible verses actual light cones. Assuming we had a ship that could go near C, imagine Alice doing three things. Alice v1 stays home. Alice v2 goes racing off near C to the left. Alice v3 goes racing off near C to the right. Each of these will have different light cones, but Alice v0 who hasn't made a decision could make any one of these decisions and thus all three light cones are in her possible light cones if she chooses to pick each action. Eventually each Alice will be so far away from each other that expansion of space splits their light cones into entirely separate ones from that point on.

>How certain are you in your reasoning?

Not at all. This is just based on my understanding of the very basics. The reason I'm sticking to it like I am is because, if I'm wrong and someone can point out where, it becomes a really good learning opportunity for me. And if I'm not wrong (at least given the layman level of detail of the conversation), the better I can explain my reasoning the better someone else might gain new ideas from it.