-자마자 is 'the instant that', and 오다 the coming: 제가 오픈하자마자 와서 'I came the moment they opened', 일어나자마자 왔어 'came straight after getting up'. It also covers something arriving rather than someone — 미끼를 던지자마자 오는 입질, 'the bite that comes the second the bait goes in'. The point is that no time at all passed in between.