Where did the tradition come from? Sith is all about betrayal and backstabbing, Thanaton liked Naga Sadow and Tulak Hord and they both did such thing.
Darth Baras let his apprentice did the same thing many times. Darth Mortis, the enforcer of law also accepted Nox and Karrid after they defeated their rival. Thanaton's "tradition" is totally nonsense.
The "tradition" Thanaton was concerned with had nothing to do with the fact that the Inquisitor killed Zash, outside of the fact that it made Zash dead. According to Thanaton, when a Sith is killed by another Sith, that Sith's power base must be wiped away. Since the Inquisitor was still Zash's apprentice at the time, he was marked for death. If instead, the Inquisitor had joined Thanaton, for example, before it happened, there would've been no rivalry. And Zash similarly wasn't punished for the same way for killing Skotia because Skotia was not her master.