Are you sure you're hearing the Auto-focus of the lens, and not the Vibration Reduction? Is it a VR lens? (Or if using a Sigma or Tamron, their equivalents to active image stabilization?)
+1 for back button focus and for individual lens calibration. The D610 can remember a different calibration number for each lens, so you only have to calibrate each one once. (For back button focus, one pro tog laughed at me and said "was that something you read about on the internet?" Another pro tog said it was what he used. Jerry Ghionis (premier wedding and portrait tog) said he doesn't use it at weddings because it makes his hand cramp doing the BBF all day, so shutter button is easier.)
One other problem with BBF is that, if you are shooting with a shallow depth of field (to get that lovely bokeh), you or your subject can move the tiniest amount between focusing and snapping, and that moves the focal plane. I hate pictures when I know I focused on the eye, but the eye is slightly out of focus, but the hair on the crown or an ear is super sharp. I've tested the lens calibrations to make sure the desired focal point is in actual focus in the pictures, so those portrait mistakes are mine. This is one problem with focusing and recomposing, because you have to move the camera body a little bit without letting your upper body or subject move forward or backwards even half-an-inch.