You go thru immgration, pick up you bags from the luggage belt and take it thru customs. After customs you turn left and walk over to the domestic end of the terminal. There you line up for the escalator or elevator and get your boarding pass cross checked with your ID by the CISF before you are allowed to go up the departures level. Some times they refuse you because the 4h rule, but if you are close enough they will let you go up. Or at most keep you in a glass walled holding pen on the departures level. Once up there, you drop the bags at the Vistara counter and go to domestic security. It could be that vistara reissues the bag tags and boarding passes.

An experience report is here: https://www.flyertalk.com/forum/31868043-post470.html