With "AF-ON only" selected for Custom Setting a4, the camera should not initiate AF when the Shutter Button is half-pressed. There seem to be just three possibilities: you have not correctly set up a4; your camera is faulty; the camera is not actually focusing when the shutter release is pressed (you might be mistaking the sound of VR for AF).
The settings of a1 and AF-C/AF-S are not relevant.
If a4 is set to SF-ON only, then the shutter release should not initiate focus. I don't see how your settings would allow "Both buttons still focus"
Don't forget that if you switch CSM banks, you must make the a1 and a4 settings in each bank.
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