After the final episode of season one I was very confused.
We know that changes in the timeline need - erm - time to propagate and settle (to give the time police and heroes a chance to correct manipulations). This time is in other cases a few hours to a few days.
Now the following happened in the end:
They managed to finally kill savage once and for all in three different times (!)
So after a few days a timeline should have manifested, where savage was killed at the earliest point in time in 1958. And from then on there is no savage and no reincarnation any more.
Beside what that means for the other two teams who go to different times to kill him, too (and all the episodes that play in a time after that) where our heroes now should arrive finding no Savage this raises the question why Rip Hunters family is not save now?
Or to be more concrete:
If there is no Savage any more conquering the world in 2166, who then kills Hunters family?
Even then, what would the final timeline be? What happens to Hunters family in it? If they are still killed by Savage, where does he came from in this timeline? And what happens to him later? If he is still there in 2166 somehow, why the team thinks that their mission is successfully done?
So, after all the things they've done to Savage, and after all the time lines have settled, what finally happened to Rip's family?