I'm asking because some screws will not go in fully flush. But I'm thinking the layer of thinset then tile will surely cover any screws that aren't flush, so tiles won't 'pop' out.
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.
They should be flush or really close to it. Especially if you are painting over with a waterproofing membrane. I throw three backer screws in a sheet and then do pilot holes with a bit the size of my head about an 1/8" in. This sounds like a pain in the butt but the extra couple minutes doing this per sheet makes setting all your screws and more important making sure your backer is flush with the wood behind it really easy.
If you don't do the pilot holes you will strip out more screws and the extra torque will pull the board from the wall.