Sometimes cancellations are automatic and the avios refund is done immediately, and sometimes they are manual so go to the back office and take 1-3 weeks. I have had both types in the past. The manual ones can be spotted as rather then just clicking to cancel you have to fill in a form. Usually these seem to be perhaps more complex bookings or partner bookings, but I haven't done enought to work out a hard and fast rule. It is not the case that all cancellations should be automatic and have instantaneous refunds though.

For the manual ones you can call up to try and hurry the process along if you are desperate for the avios back. If not just be patient and keep a note to check in a few weeks. All my manual ones did get refunded in the end without intervention by me on the phone.