Everyone does it differently, of course.
The few I have shipped this fall were soaked in a bleach water solution then dipped in a fungicide solution before allowing to dry. Sometimes I dried overnight and others I dried just for a few hours.
I have had someone ask me not to dip in a fungicide.
Now how long to soak in bleach water depends how long you want or need to. One person I know soaks them for 30 min to get the roots as white as possible then dips in fungucide to kill anything because once they go into a dark, sometimes damp ( if not completely dry), and hot (depending on when shipped) enclosure of a box; it can be a good breeding ground for fungus or mold.
Others only use the bleach water while some only use a fungicide because they say the bleach stresses the daylilies even more. I have heard of some doing an insecticide as well. I have gotten some that probably had none of the above. Some people dry them completely before shipping while I have gotten them and the paper is damp so they weren't completely dry ( I believe some keep them damp on purpose so the roots don't dry out too much).
There are a few people on here who ship daylilies so I'm sure you'll get plenty of replies.