I've never transferred from RBC to Asia Miles, but I have moved from RBC to BA, and that posted within a day or two.

For BA it is NOT account agnostic - the member receiving the points must be under the same name as the credit card account holder. RBC agents will take the number, because they don't know the name of the account attached, but it will be rejected by BA once the request is received.

Not 100% certain it's the same for Asia Miles, however.