Ignore audio pronunciation in this case.
You're exactly right, it should sound like the short vowel, rhymes with sub, dub, "ub".
There are two a vowels in Hindi, one is the schwa, which is this word, "ub" rhymes with sub.
When transliterated in roman letters: Often, the short a vowel is written with a single U, and very often with a single A.
Proper names might vary a bit, but the reason you see the double-a in Aamir is because it's the long