number of blood slaves in sacrifices and their success

[tinkthank]

Obviously I am too dense to figure out how the mechanics of blood sacrifice works.
Choosing Mictlan (so that I can make sure no dominion increase comes from extraneous effects), I give a Mictlan priest in a province with a temple three blood slaves and a lab and set him on "perform blood sacrifice". Host.
The next turn, I see he *still* has *three* blood slaves in his possession. The dominion has not risen. He is not set on defend, but rather still on "sacrifice". I am confused, try again. Host.
Next turn, he *still* has three blood slaves, but the dominion has risen by 1. Confused. Host.
Next turn, he has *one* blood slave, and the dominion has not risen.
Very confused. Not hosting.
I had thought: Me give priest X number of slaves. Priest kill dem good, one after de other (x-1 per turn). Sometimes dominion rise, sometimes no. When priest got no more, he stop.
Me be wrong. Right?
So....
- can a priest fail to perform a sacrifice at all? (i.e. not only not raise the dominion, but not kill any slaves)
- or is a slave only killed when the dominion rises?
- or do sacrificing priests get new slaves automatically from a lab if they have access to one? Or always, no matter whether access or not?
- or something completely different?
I would be happy to be pointed to a guide, which I have not found by searching, or simply a few friendly tips. Thanks tons.