Furigana in depth
Over each kanji or over the whole word
There are two ways of placing the reading. One splits it character by character, so each kanji carries only its own part: に over 日 and ほん over 本. It is the one that teaches most, because it shows which reading each character has inside that word. The other puts the reading over the whole group, and it is required when the word cannot be split: in 今日, きょう does not divide into one piece for 今 and another for 日. In both cases, the hiragana after the kanji has nothing above it.
Hanasuka uses the second, out of caution: each group of consecutive kanji carries a single reading, because splitting it character by character would require knowing where each word breaks, and that would already be guessing. Nor is the reading worked out by any dictionary: it comes from the one each sentence has written in kana, and the app only distributes it after checking it fits the text. If it does not fit, the sentence is drawn without furigana and the reading appears in full on its line below, because for learning a wrong reading is worse than none.
When furigana says something else
In fiction furigana is also a stylistic device. The author writes the kanji for what is meant and above it the word that is pronounced, and so gives two layers at once: 本気, «seriously», with マジ above it is how a young character says it, and in science fiction or songs 宇宙, «universe», sometimes appears with そら, «sky», above it. In song lyrics it happens often, and what is printed does not match what is sung. For the learner it is enough to know it exists and not to take those readings for dictionary ones.
The other ground where furigana works every day is proper names. The same surname written in kanji can have several readings, and given names allow unusual readings chosen by the parents, so not even a Japanese person takes for granted how someone else's name is read. Hence class lists, signs with names and many business cards carry the reading. For the learner the lesson is practical: faced with a proper name, you do not work out the reading, you ask for it or look for it written down.
How to wean yourself off it
Furigana is an aid you withdraw, and the mistake is to remove it all at once or never remove it. What works is reading each sentence twice: first trying to read the kanji without looking at the line above, and then checking. The words that come on their own no longer need the help; the ones that do not, still do. Over time your eyes stop drifting up, and that is the moment to switch it off and see what happens. If reading turns into constant stumbling, you switch it back on, no problem at all.
In Hanasuka the switch is in «Your account», next to romaji and text size, and it is saved with your progress. When you turn it off the reading does not disappear: it drops to a line below the sentence, so you can check it without it sitting above the kanji. Where the reading would be the answer, as in the kanji reading quiz, it never appears. And the kanji listing lets you search by reading, which is the reverse route: from how it sounds, find the character.