Viviana’s death is natural. Remember last chapter Ines remembered Viviana dies from tuberculosis previously. Ines knew she would die but it seems as though she forgot since she was dealing with many things. So, no, Oscar had nothing to do with it. Viviana’s fate is to die during her teenage years. Oscar is just smug because he believes he’s superior to those who do not have memories. He thinks of the people whose fate it is die as shadows of themselves. In a way, he sort of has a god-complex because he thinks he knows the future. So his statement at the end is another confirmation that he knew Viviana was going to die and he knows if she lived a little longer this time around in contrast to other timelines.

Maybe I’m being paranoid, but Vivi’s death was not natural. It feels premeditated…
Can novel readers please spoil?