When installing backer board for wall tiles, do the screws need to be absolutely flush or even pushed into the backer?
Since you will be applying thinset and tile, you have a lot more "play" in your screw head depth.  While you of course want them to be as flush as possible, the tile over thinset will even things out as you apply the tile and make them flush.

If this were drywall, the story would be different.