First things first: there is no time travel. Learning the alien language alters the way you perceive time, allowing you to experience "memories" of future events. It's as much time travel as remembering your birthday party from last year is "time travelling" into the past.
Secondly, we need to separate Louise-the-Narrator from Louise-on-screen. Louise-the-Narrator is speaking from a specific moment in time, presumably AFTER everything we see on screen has happened. At least, that's how it usually goes for movies that have a character narrating stuff in voice-over.
The first thing Louise says is "I used to think of this as the start of your story" (or words to that effect):
Referring to her daughter's birth. We then see a series of excerpts from her daughter's life, where she progressively gets older and eventually gets sick and dies.
After those scenes are over, she says something about realizing that the story of a person's life need not be restricted to the time that they're alive. That a person's existence can influence things outside their own lifespan.
The implication being that her daughter's story should include the events which are then told over the course of the rest of the film. On first viewing, we naturally assume that Louise means her daughter's life and early death will somehow influence what happens between her and the aliens, because at this point in the movie we're assuming her daughter's life happened before the aliens arrived.
Louise-as-Narrator is actually stepping back to events which occured before her daughter's life. As we realize later in the film, Louise's daughter hasn't been born yet, and that what she actually meant was that her daughter's story began before she was born.
All of this is over and done with by the time Louise-as-Narrator begins speaking. The part about the Chinese ambassador meeting her at the book signing might still be in the future, but by the end of the movie she can remember her whole life, so that's not much of a limitation on her abilities as a narrator.
This might even be something she's telling to her daughter, as she lies dying in the hospital bed. Explaining why she did the things she did - how she met Hannah's father, why they divorced, etc. This part is, of course, pure hypothesis on my part.
TLDR; Louise-the-Narrator is the one telling this story, from a specific moment in time for her character. All the scenes in the movie are shown to us in the order she chooses to recount them. The movie doesn't really specify when Louise-the-Narrator is speaking from, but as long as it's some point after she gained the ability to "remember" the future, it doesn't matter. She can then recount any event that has happened - or will happen - in her life. *
* Subject to her ability to remember them. We know memories of our past are not perfect, and it stands to reason her memories of the future will have similar flaws or gaps. But obviously she remembers everything she tells us in the movie - at least, she never gives us any reason to think she's an unreliable narrator.