Somebody go make Trombone Hero immediately.
They have the same illogic with time travel as the Flash.
The things around them change, even Steel's hairstyle, yet they personally aren't affected by the timeline changes as they have no idea about all the changes.
I can see in the ship they should not be affected being outside of time - but then stuff like the video game and the rat's name shouldn't change either.
or in the episode with the Vikings - the Time Bureau people were all affected by the changes and you would think they would be protected.