(I'm a co-founder of Balanced, a payments company also building push to card (p2c) functionality [1])
> There's no way to map debit card numbers to routing/account numbers (afaik).
You're correct.
> They're probably using the ATM network primarily and another method if it's not supported.
Based on the settlement times advertised, it looks like Stripe is simply performing "unreferenced refunds" to debit cards, rather than using the various ATM networks to push funds out to cards. If they were using the ATM networks, you could expect sub-10 min settlement times.
I mean, the funds will be available for use in the recipients bank account within 10 minutes. The API call to perform this operation will have much lower latency than that. Did I understand your questions correctly?
[1] https://www.balancedpayments.com/push-to-card