Sometimes in Japanese, you'll find words that break the traditional rules of what you would expect to be correct. Certain uncommon readings are given to words that neither match the Onyomi or Kunyomi of the Kanji. However, it is important to note that in the word 大人 the word is read as a whole. Consider that 大 is not read as お or 人 as とな; no, these Kanji are only read this way in this particular combination. I am not exactly sure why this may be, but I am going to speculate based on what I heard in former Japanese courses. Kanji is a system that was imported into the Japanese language and is based on Chinese. You probably already know this, but this I think this is important to note, in order to realize why some words may be read differently than you might expect. Before the Japanese people borrowed Chinese as their writing system, no writing system existed and during the conversion process of Chinese writing, some Japanese words resembled their Chinese equivalents due to China and Japan having history together. For this reason, you'll notice some parallels between Chinese and Japanese readings. Example: 天気 (てんき） - Chinese reading = tian qi The resemblance is very slight, usually, but it's there. In some cases though, you'll find words that don't resemble their Chinese counterparts at all. The word has a pure Japanese reading. The purely Japanese word was given Kanji to show it's meaning, since Kanji are like units of meaning, rather than a letter in an alphabet. Another example of words like 大人 is 明日 (あした). This word is only read as あした when those two particular Kanji are paired. It could have been read as めいじつ, perhaps, but that word in Japanese does not exist. So the word was given a Kanji that matches or approximates the meaning of the word.

What you say is correct, those are the right onyomi. But, this word is pronounced as おとな. I have never heard anyone pronounce the word as だいにん. おとな seems to be far more common if だいにん is even something people say at all. A native speaker probably has more personal experience and could add extra information on that. There are many jukugo who do not follow the onyomi. Sometimes the exceptions have readings which are close to the onyomi, sometimes the kunyomi is used instead, or in cases like this, neither. Some examples: Name. All kunyomi. 名「メイ」　前「ゼン」　名前「なめえ」 Completely different, neither ON or KUN.　今「コン」　日「ジツ・ニチ」　今日「きょう」 There are cases where words have extra readings, but there usually is one reading which is more common than the rest.