I've come to the conclusion that this game is probably not in the Child Timeline. This comes from discussions on a subreddit that analyzed that speech of Zelda's and the vernacular of Twilight Princess, both in Japanese. When Zelda mentions "twilight" in that speech, she uses the word "tasogare" (黄昏), whereas the Twilight Realm is Japan is known as "kage no sekai," or "Shadow World" (影の世界). Apparently, the only time "tasogare" is used is Midna's "Twilight Princess" title. And no, the Japanese title doesn't use the word either, instead just calling it "Towairaitu Purinsesu" because Nintendo of Japan is silly.
You know where else the word "tasogare" was used, though? In the manual of A Link to the Past, referring to the Sacred Realm. In the same passage that the NoA manual translates as:
Admittedly I haven't seen if this word was used again in the actual game text, and manuals aren't necessarily the best indicator of canon, but it is interesting to look at.
Based on this, though, I think the "twilight" reference is indeed just a cheeky reference and nothing more; the same speech apparently mentions "crossing the seas seeking the gold of the gods," which for all some know is a reference to Wind Waker, so it's not like that speech is definitive proof of... anything. Meanwhile, there's the tablets talking about Ruto's ascension as a sage and aiding a princess and an ancient hero against what's implied to be Ganondorf... that didn't happen in the child timeline.
It was also mentioned in-game that each Divine Beast was named after a Sage too which means Adult Timeline somewhat, so I don't know either.