Best and surest way to confirm a cancellation is to log out and then log in again into your LM account while still on the phone (after she/he asks you what else they can do for you, ask them to wait while you confirm the miles are back).
Never hung up the call before confirming the miles are in your account.
The BS about miles taking time to get refunded is, BS. If the miles are not back, it means the refund wasn't successfully transacted. Continue with the call and ask him/her to double check.
Once miles are back, then taxes deducted and fees charged will show up on your CC eventually.