Humanity, with modern science, has established that the Big Bang happened 13.8 billion years ago. The universe appeared in a low-entropy state, and for billions of years has been expanding and moving to a high-entropy state. We await, and dread, the heat death ahead of us... and the end of all life.
One day, we discover a civilization that perceives time in the opposite direction. They have, with modern science, established that the heat death happened 10100 years ago. For them, the universe appeared in an extremely random and large state, and they're terrified of the Big Bang coming up in just 13.8 billion years.
Is this realistic? I understand that physical laws are valid in both directions of time, and that's why I'm asking this question. I can't imagine how a biological system could have memory of the future. Even with the computing tools we have today, it's very difficult to study the future, whereas it's relatively easy to study the past (e.g. we know much about the history of life thanks to paleontology, but we know almost nothing about its future evolution).
I'm also wondering how humans would communicate with this kind of life. What we see as "first contact" would be, for them, the end of contact. Before we even meet them, the aliens would know everything about us, and our entire shared history. Including how we watched them devolve, technologically and biologically. Standing on even footing with them, at any point in time, would be incredibly difficult.
EDIT: I think some people may have misunderstood the question. To clarify, these aliens see the universe as contracting, as entropy in an isolated system going down, and as room-temperature water spontaneously freezing into ice cubes. This is because they have memories of the future, not the past; there is no "reverse time flow". This takes place in our universe, and time works exactly as it does now, on Earth.