If you fill to the top, it will not carbonate.
I think the wand leaves the level too low. When filled, I touch the wand against the side of the bottle and let it fill to about half to 3/4 inch from the top.
The less air space you have, the less O2 you have in the bottle.
I don't think it is best practice to fill to the same level as Commercial brewers, some of those bombers have a couple of inches of airspace in them. I think Commercial brewers squirt in a jet of water just before the cap is put on and sealed. This jet (of whatever it is) makes some of the CO2 come out of solution and fill the headspace at the top of the bottle eliminating any air in the bottle. The bigger space you leave in the bottle, the more O2 you are leaving in there ..... and we know O2 is not good for beer.