Madrasi, also spelled as Madrassi, is a term used as a demonym and sometimes a regional slur for people from southern India, especially Tamil Nadu.[1] In earlier usage it was a demonym to refer to the people of Madras Presidency, including the people of present-day Andhra Pradesh, Tamil Nadu, and parts of Karnataka and Kerala, however this use of the term is now outdated.[2][3][4][5][self-published source][6] In present-day, the exonym Madrasi specifically refers to the people in living in Madras (officially called as Chennai), and the term Chennaite (or Chennaivasi) is the endonym for the people living in the city.
Madrasi is a reference; it could be also a 'regional' slur
Although "Madras" is the name of a place, in this context it is used as an adjective and not as a proper noun.