Time travel is real and it is happening before your very eyes. Every satellite in earth's orbit travels slightly in time, which is precisely the reason why they have to adjust onboard clocks to atomic clock here on earth. That idea is at the very heart of theory of relativity and we know that that theory is solid hard and proven beyond any reasonable doubt.
This isn't the Time Travel I am referring to broadly. What you are actually describing is the dissonance between two standards which self-reference in discussing each the other.
This flux is hardly the classic Time Travel of my heading which intends to say you can't go back to the time of Abraham Lincoln and stop John Wilkes Booth from pulling the trigger.
Context is everything.