You get the 96 hr free transit once (either on outbound or return, if its a one way then you still get it). If its same ticket - you wont have any issues at check-in India. If India-Sin and Sin-US are on separate tickets, carry a printout of the rules from ICA website.
Make sure you have a blank page on passport, they actually put a big visa stamp and then another to mark the entry which takes the entire page.