Autosexing breeds like Bieles and Legbars can get a bit tricky to determine the sex of at hatch if the autosexing trait isn't well selected for, but it's mainly in that you get more chicks that kind of fall in a gray area of could go either way. You select for better autosexing traits by just not keeping the ones that are more ambiguous and only breeding the ones that are obviously male or female.
Mixes that are sexlinked crosses, those sexlinked genes will always be inherited a specific way, it just doesn't work, or not as well, when you add certain genes that cause chick down colorations that make it hard to tell whether the gene was inherited or not. As an example, if you have a non-barred dominant white rooster that you cross to a barred hen, the male offspring will inherit barring and the female offspring will not, but male or female they will also inherit dominant white, which makes the chick down entirely or almost entirely yellowish or white, so the head spot is simply not visible. That, of course, is an extreme example, but pretty much any chick down coloration that is not black on the head can result in the barring head spot either being faint or simply not visible at all.
There is no improvement of sexing quality for the next generation in such crosses because they are just that, one-time crosses. You can't select for better sexing because crossing the resulting offspring of the original cross will not make more sexlinks anyway. In order to produce sexlinked crosses that are reliably sexable at hatch by these traits, you have to use birds whose genes will not result in chick down colorations that obscure the trait at hatch. I hope that makes sense!
As far as whether the hatcheries vent sex their autosexing breeds, I have no clue, but that is an interesting question
