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I see this written in furigana and hiragana as 'あいて / aite'. However, every source I have looked at also seems to be pronouncing it with an additional syllable before it making sound as if it were 'ひらいて / hiraite'.
What is going on here? This is the first time I have encountered a word that wasn't pronounced exactly as written in hiragana.
開く actually can be one of two words: 開く{あく} and 開く{ひらく}. These are separate words that have slightly different meanings (but they both typically translate to 'open'). It seems you were thinking of the former, あく, but you actually found the latter, ひらく.
開くwould have solved it.