How do I ask for reviews from stories without sounding pushy?

Ask for the review the next day, from someone who already came, with the link and a short line. A five-star sticker on the same day as an offer sounds like pressure. Have the direct link to the listing and send it only to someone who has already been, not to the whole story audience. The review is requested on the same story as the discount, and someone who has not visited yet stops trusting it. You leave with a follow-up story, link and one line, to use the day after the visit.