Tatties were the Indian equivalent of the air-conditioner.
Damp screens hung over the openings of the house, which along with the punkah (a large fan operated by an elaborate system of pulleys, which the punka wallah had to work) could keep a house quite cool.

BTW I'm not entirely sure Gunga Din is a colonialist view of lower orders.
Gunga Din would have been of a very low caste (had to be to serve water to the British) and despised by all, especially his own countrymen. So here you have someone with every reason NOT to be a good man, yet is.
Now, the narrator makes no excuses, expresses no regret, yet is quite honest.