The ticket is sent to the outport reservations centre of where the ticket originated. I was told it can take anywhere up to 3 weeks.

On the other hand, if you want the miles back now you can ask the KF service centre in Singapore to refund the ticket (miles and taxes) on the spot. The downside is that you might take a forex hit because they do the refund based on SGD rather than whatever currency your ticket was issued in. But for urgent redeposits (e.g. because you are eyeing another award) I think it is worth the small hit.