After her core was extracted, her physical body was possessed two times. The First time, the Necromancy King performed a forbidden ritual on her and made him his undead general, and the second time, it was the old witch who used witchcraft and used her as her battle puppet.
The after-effects of those rituals probably brought some undead abilities in Alina which were boosted further by repair of her body parts and insertion of her old core.
Since Mark didn't exactly know what happened with her in the past and neither did Alina remember anything as her memories exist in the core itself, he could only assume that it was for the best and put those unnecessary thoughts for the future away. Mark tested her abilities for a while before taking back her with him.