Various characters say "come back in X days".
Great question, me. Here they are. The +n days means that many days after you first start the demo. The specific dates given are assuming you started the demo on October 18th, otherwise you'll just have to add it up yourself :)
+1 day (19th Oct): talk to guy outside outside Pokecenter to receive 10 Pretty Wings.
+5 days (23rd Oct): talk to the girl in the south west of Hau'oli City.
+12 days (30th Oct): talk to guy with Pikachu in Hau'oli City Hall (middle of town) to celebrate Pikachu's birthday.
+18 days (5th Nov): talk to the police officer at Hau'oli City Marina (south east).
+24 days (11th Nov): talk to girl in the Ferry Terminal by Hau'oli City Marina.