Confused About Standard IPA

The range of sounds denoted by the symbols of the IPA are defined by the International Phonetic Association. Consider the T sound: it is pronounced differently in tick (aspirated as [tʰ]), stick (unaspirated as [t]), latter (flapped as [ɾ]), and pat (unreleased as [t̚]). The IPA is an International Phonetic Alphabet, which means it has different symbols for each sound.

However, this is not how you expect a pronunciation to be denoted in a dictionary, which traditionally use phonemic systems. Such systems represent all the different ways a phoneme can be pronounced with a single symbol. The International Phonetic Association does not define how IPA symbols should be used for representing phonemes, which is what you are asking for. Indeed, there is no universal system for representing English phonemes, and there is no institute or academy that regulates English to decree one, either.

As you have discovered, the result of this situation is that every organization that has needed a phonemic system for representing English has had to borrow someone else's system or invent their own. Though they generally overlap in much of their symbol choices, there is no universal standard for the representation of English phonemes.