Can I ask a DST INSPIRE faculty for a recommendation letter? I will be applying for PhD in USA this year, so I will be needing recommendation letters. Can I ask a DST INSPIRE faculty who used to work in same lab as me (apart from my principal investigator)? Will US universities consider this reference because I don't know if they are aware of what is a DST INSPIRE faculty. Will it pose a problem because DST INSPIRE faculty have a tenure of 5 years and I don't know if will they become permanent after that. Also, they are not given the designation of an "assistant professor" and are call "DST INSPIRE faculty" so I had this question?

DST INSPIRE faculty: It is a scheme by the Department of Science and Technology (DST) to offer an opportunity to young talents in India through contractual and tenure track positions for 5 years in both basic and applied sciences area. And INSPIRE means Innovation in Science Pursuit for Inspired Research.
In general, any mentor with good scientific or academic qualifications can be a good recommender.  It's always better to have somebody who can speak strongly about you, even if they're in a "non-standard" academic position.

That said, it's important that your letter-writer make it clear who they are and why their opinion should be taken seriously, especially when writing to an international recipient who may not know their system.  That might include explaining what a "DST INSPIRE" faculty position is, or it might just mean pointing at the letter-writer's own CV of scientific accomplishments.