Though as I alluded to earlier, there is no certainty that Petofi died. In fact, the show deliberately makes Petofi's fate a mystery. He could have died in the fire in 1897 - but it's just as possible that he was able to escape and is still very much alive somewhere in 1969. So, we cannot establish anything one way or the other when it comes to Petofi's potential continued influence.
Something also to keep in mind is what transpires once[spoiler]Chris tracks Tate down and what Tate is still quite capable of doing.[/spoiler]But we won't see that for several more weeks...