How soon should the core offer be presented after someone has purchased the tripwire?

Upon the checkout of the tripwire you would show someone an upsell for the core product.

You can use tools like ClickFunnels or SamCart to do this. If someone doesn't buy your core offer right away you would want to continually email them with different approaches for the next week or so to get them to try and buy your core product. Such as emailing them a case study of how the core product helped someone and the results they got.