No, Lucy didn't travel in time (although, it was my first thought as well), nor did her mind re-enact those events. She remembered them.
Throughout the film, professor Norman explains how the purpose of life is to pass on the knowledge through time. From the first cell, its splitting in two, and on to the more complicated life forms, the purpose is always passing the information.
Also, among the first changes that Lucy experiences is her remembering her own early life (the cat that she had when she was one, her mother's milk,...) which she reveals in her phone conversation with her mother. Later on, that remembrance then spurs to the earlier events (her own growth of bones).
The "time travelling sequence" that we see is the process of all life since its beginning, in reverse. It does not end with the Big Bang. It ends with many cells connecting (back) until there is one left, which was the first cell ever. The whole sequence is Lucy remembering all the knowledge that was passed from that first cell all the way to her today's cells, and conveniently saving it in some form on a computer.
Addendum: It was noted in the comments that she had some interactions with history's beings (Indians, dinosaurs, human ancestors,...) and that we see her in those interactions, not her own ancestors. The way I see it is:
The memories are someone's. They acknowledged that person, not Lucy. We see her because she's remembering it.
I think it would've been too confusing if in each of those short interaction scenes we saw the actual ancestor, and the fact that no one seemed alarmed by her sudden appearance (which would be a necessity if she time-travelled) makes me more certain that those humans and animals interact with someone who was naturally there.