Mine had a different experience. She was a strong, multi-year L10, but not one of the best. So not someone who was getting a bunch of offers on day one, but also not one who was ignored and happy with anything she could get. For gymnasts like her, they are sort of "2nd tier," which means you maybe get some attention but not commitments from the highly ranked schools, and more attention from lower ranked schools (who tend to recruit later and more slowly.) It's not the best situation, because you don't get a bunch of offers to consider simultaneously, yet when you get an offer it's hard to know whether to take it or wait for something better (e.g. the schools who are talking with you, but back burnering you likely until they hear from their top choices.) If you wait, the offer(s) you have may disappear. But as the offer is not really what you want, and your top schools are still talking with you and haven't said "no," it's hard to take it, especially early. Some schools will tell you right away if they are taking a pass, which is actually great (as hard as it may be, especially if it's the dream school.) But others will keep you hanging on, thinking maybe you have a shot, but not making the offer, even when you have to decide on the other, "lesser" offer.
My kid's experience might not have been the norm, but I feel like those most willing to share their experiences are the ones whose journeys are super straightforward and seemingly ideal -- calls and some offers from all their top choices on 6/15, home visits from said schools in the summer, back-to-back official visits in September/October, and then weigh the offers and commit.
In terms of your specific question, my daughter got most of her offers at a meeting with the coaches on the last day of her visit. She got some offers on the floor right after Nationals. She also got one or two on the phone, I think after the visit.
I hope this is helpful to some who may be in a similar position.