Think about numbers, it is not sorted phonetically,
Even the alphabet is not. All those languages that use alphabet sort in exactly the same order regardless the pronunciation.
Point being: kanji words aren't always sorted phonetically, for the reasons described in the article, so a user may not be surprised if they aren't. But when a human is sorting kanji words they do so phonetically by reading.
Yes - or that's how a human would sort them, at any rate.