If by IPA you mean the International Phonetic association, that does not dictate how words should be transcribed. It created, and has several times updated a list of symbols representing all the known and most of the possible sounds in all human languages. [æ] (in square brackets) is one of these symbols, and any trained phonetician, whatever his or her nationality will be able to produce exactly the same sound when s/he reads that symbol. It is not, incidentally, the sound that many native speakers produce in 'bat or 'man'.
If by IPA you mean International Phonetic Alphabet, then most untrained people do not use it. What they use is a set of phonemic symbols borrowed from the IPA. For each sound, linguists within a country pick an IPA symbol, usually either one that is a letter that frequently represents that sound normal orthography as with the /e/ that most (not all) British course books and dictionaries use for the vowel sound in 'dress' and 'bed', or an IPA symbol that is very close to the native English sound, as with many of the consonants.
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