There's just not many reasons why she couldn't have come up with the title by herself
It's not really like "eyes" "smoke" or "magic" are english words that are uncommon or anything by Japanese standards...they're actually probably everywhere.
So when someone comes along saying that Timmy influenced her, without any hard evidence except "I don't think she could have come up with it on her own"...It just sounds like the common stuff other people say.
idk personally, I'd find it hilarious if Timmy named his own composition that...I don't really feel like it suits his personality at all...but then that's just my opinion as well.
You guys could ask him~