OK, yeah, that’s a good and interesting question. And let's make it clear first of all what order things happen in. If I say "no sooner had I arrived at the station than the train came in", we need to be clear what happened first. Does it mean, the train came in and then me, or I came in and right after me the train? Well, my experience is actually that I arrive at the station, and then the train doesn't come in for hours. But, to answer your question, if I say "no sooner had I arrived at the station than the train came in", it means, I came in, and right after me the train. I got there first, just. I'll give you another couple of examples. No sooner had I put the phone down than it rang again. No sooner had I finished the meal than I started feeling hungry again. It's actually a rather literary construction. I'd expect to read it, maybe write it, but I probably wouldn't say it. Instead I think I'd say something like this. "The train came in just after I got to the station", or " I had only just got to the station when the train came in" or something like that.