From a Gatherer ruling on Altar of the Brood:
9/20/2014 If Altar of the Brood enters the battlefield under your control at the same time as other permanents, its ability will trigger for each of those permanents.
Like the ruling states, all the Altars would "see" the other permanents that come into play at the same time. You would mill X times the amount of Altars in play, and that includes the Altars that come into play after you sacrifice Pyxis. X is equal to the number of face down cards exiled with Pyxis of Pandemonium.
In addition, what of the zombies resulting of that mill? Would they be
a separate resolution following everything in the Pyxis resolving or
would they resolve within the Pyxis? Also would they then include any
Altars and Pyxis that resolved in the Pyxis?
The Undead Alchemist's second ability is just a plain old triggered ability. You will have a whole lot of Altar triggers that mill cards. Every time one of Altar's triggers resolve, you mill one card. Then, if it is a creature card, the Alchemist's triggered ability triggers.
Remember that although the Pyxis will put many things on the battlefield at the same time, all these triggers have to be put on the stack one by one. They do not resolve as a group, but one at a time after priority has been passed by both players.