The key is not "Be on your guard!" but rather, "The dragon is poised to swoop!" which implies "don't stand in the middle", as many circular arenas have dashes/swoops through the center. The side effect of leaving the middle is that you have roughly a 1/8 chance of finding the dragon without actively searching for it or being told to, and after two runs, most people should have had an epiphany and discovered the implied instruction, "find the dragon". As you said,
so it appears that after two runs you had this same epiphany, so I don't find the text problematic at all. Mechanics don't need to be obvious the first time. It's okay for them to take two runs to figure out.