I can see that the word postman is pronounced as /pəʊs(t)mən/ commonly, where you can’t hear the vowel in the ‑man syllable.
But sometimes it is pronounced /pəʊs(t)mæn/ — with a noticeable /æ/ vowel like in the word man — as heard in the 1961 song “Please Mr. Postman” by the Marvelettes from more than fifty years ago.
Why is postman sometimes pronounced differently in different times, places, or situations?
What is the real pronunciation of the word?
There is a fair amount of variation in the pronunciation of words ending in -man. Dictionaries usually try to indicate the most common variant first, but in most cases there is no special reason to call the most common variant the "real pronunciation" or anything like that. Both pronunciations are "real" (at least in the most literal sense of the word). If you feel uncertain about which pronunciation you should use, though, it's probably a safe bet to go with the most common one.
Merriam-Webster for example says "\ ˈpōs(t)-mən , -ˌman \".
Mark Liberman wrote a Language Log post in 2015 about this topic: "Man: reduced or not?" Liberman says "the distinction looks pretty arbitrary to me, in synchronic terms"; a later comment by Jongseong Park cites John Wells's Longman Pronunciation Dictionary as saying
-man mən, mæn —This suffix may be weak or strong. (i) In most well-established formations, written as one word, it is weak, mən: policeman pə ˈliːs mən. (ii) Where written hyphenated or as two words, and in new formations, it is usually strong, mæn: spaceman ˈspeɪs mæn. Note batman 'army servant' ˈbæt mən, but Batman (cartoon character) ˈbæt mæn
