The Doctor had noticed new people on the island. He was just busy. You know, busy, that thing he was when he wanted to ignore something. Then morning came and he suddenly wasn't busy. That was why he was sitting out on the grass in his deck chair wearing sunglasses and enjoying a drink with a little umbrella. Yes, it was morning. No, there was no alcohol in it. He was a teacher. He was supposed to set an example or something. Then there was that part about meeting parents (which he was never really fond of), which was why there was a handwritten note on the door of his office informing anyone who wanted to see him to come to the park and look for the big blue box.
That would be the time machine posing as a big blue box that he was sitting next to.