What auto delivery really is
Some listings are code-based: the seller has loaded a pool of unused codes in advance. For those, the moment your payment is confirmed the system takes a code from the pool and puts it on your order. No one has to wake up.
If the pool has run out, the line simply waits and the seller sends it by hand instead. So a listing marked instant can still take some time if stock ran out.
What manual delivery is
Everything that is not a stocked code is sent by the seller: a top-up credited to your UID, a subscription activated on your email, an account handed over. The seller opens the order, does the work, and writes the result into the order.
A seller cannot see anything you typed until the payment is confirmed. On a mobile payment, that clock does not start until the transaction is matched.
The waiting time you should expect is the one shown on the product page — each seller sets their own. There is no single site-wide delivery time.