I played this sentence for about 10 times now... I hear "मैं शेहेर में रेहेता हूँ", is the audio correct?
From the little I've read about Hindi pronunciation, the inherent vowel does indeed 'misbehave' in the vicinity of ह.
When an "h" is surrounded by two short "a" sounds like in बहन or शहर , it the a's become more like e's.
That's incorrect/odd in English although it's a common Hinglish expression. रहना means both to stay and to live, but when you talk about the place you sleep, you say you live there.