I have a CX (and hence Asiamiles) account.

I recently booked CX flights online (web) while logged in and added my BA executive club number. Using the browser or the iOS app (also logged in to my Cathay account) correctly shows all my flights and the BA number.

I do this once a year and have never had a problem. Nothing ever gets credited to Cathay, and the avios (and tier points) always credit correctly to BA.