Effects of global warming on drought in India
Since you asked for an intuitive explanation, my thoughts would be that due to predicted increasing sea and global temperatures, the models used might be predicting a corresponding increase in monsoonal moisture or duration. 

From Climate of India :


  In India a tropical wet and dry climate is more common. Noticeably
  drier than areas with a tropical monsoon climate, it prevails over
  most of inland peninsular India except for a semi arid rain shadow
  east of the Western Ghats.


An article on 
 the National Geographic site discusses the relationship between the ocean air temperature and the monsoons in India:


  The summer monsoon is associated with heavy rainfall. It usually
  happens between April and September. As winter ends, warm, moist air
  from the southwest Indian Ocean blows toward countries like India, Sri
  Lanka, Bangladesh, and Myanmar. The summer monsoon brings a humid
  climate and torrential rainfall to these areas.


So in a region which is warmer, both air and ocean temperature, this monsoon effect is apparently predicted to be altered accordingly, resulting in either a higher precipitation, or longer duration to the wet cycle, to effectively make this region wetter than it is today. Without knowing more about how the models were derived, this is just speculation however.