This particular lab happens to be primarily privately funded, donations, grants, etc,. Most big ticket research at IITM like this one are industry-funded or donation-funded. The public funds cover all the usual stuff and I don't mean to understate it.
Oh, I could find just the founding statement of the project stating it was funded by the “Principal Scientific Advisor” of the government of India https://acr.iitm.ac.in/iitm_in_news/iit-madras-launches-sudh... did you find something different?
Edit: it seems you were right. Apparently they have received big donations from ex-alumni including the co-founder of infosys and the founder of Fairfax Financial Holdings. Pretty cool!
The article you linked to itself states;
The centre will power a large-scale multi-disciplinary effort to map human brains at cellular level. It is supported by Infosys co-founder and IIT Madras’ Distinguished Alumnus Kris Gopalakrishnan and his wife Sudha Gopalakrishnan. Since 2014, Gopalakrishnan has been involved in seeding research at the institute at the intersection of neuroscience and engineering.