Why do students from NSIT, DTU, IIIT A, IIITD and MNNIT perform well in SPOJ, CodeChef, and Codeforces even though NIT Trichy, Warangal, and Surathkal have much better ranked students?

Competitive coding has nothing to do with the JEE curriculum. So someone’s coding skill does not depend on their JEE rank. At least not until coding becomes a part of JEE syllabus. 

Coding depends a lot on the environment of the institute. Environment plays a major role in making students do certain things. IIITA has a great coding culture. Which makes everyone have a go at coding. It’s the culture that provokes you to start competitive programming early. You will not find that kind of coding culture at most NITs.