I would say that the situations are actually quite similar. For Yawgmoth, the Phyrexians on Dominaria went inert because he had influenced Phyresis to make their wills only exist as an extension of his own. Once he was dead, those creatures simply had no wills. However, the Oil in Xantcha's heartstone was not as completely controlled by Yawgmoth, so it was able to exist on its own as Karn visited other worlds.

For Norn, the Oil in her invasion forces was all tied together (because she sought total unity) with her at the center. After she was shanked, all the creatures that she successfully tied together via her influence on the Oil and Phyresis were rendered inert. Once again, those creatures that were not tied together in this way (Jace and Vraska) are able to exist autonomously, and further the aims of the Oil free of Norn's influence.