I'm not an SP, but I will say that I'm actually very aware of my surroundings. Which is one of the reasons that I need fairly quiet environments with a minimum of distracting movements and noise. I notice EVERY LITTLE SOUND, and it can get annoying. I end up shouting at people sometimes, "Hey, stop that racket! I can't think with all that noise you're making!" And then they'll say, "But all I did was throw an empty cola can on top of another one!" Yeah, it gets especially bad at night for some reason.
Oh, and there's another one I do. I see someone suddenly going to grab something within my field of view, and I start going, "What are you going to do? Why are you touching that? Be careful not to mess with it too much, I might need it for something later."
Of course it's even funnier when I see people doing something outside their normal routine, I go, "What are you going to do, and why are you doing it?" I'd probably make a good security guard, LOL.
I have noticed that I really only do this in my own home, though. I think it's got something to do with the fact that I'm more "in my mind" at home, and resent the intrusion of any external stimuli. If I'm focused on doing something rather than thinking, like I typically am in public, I still notice but it's not as much of a problem.
I imagine that if inferior Se makes me that aware of my surroundings in a negative, paranoid way... SPs should not only be aware, but have a more refined, comfortable awareness.