I pick up my STPC vouchers either at SFO or CCU, my origin/dest airports, for my Dubai stopovers.
From the US, I always book the STPC stay on the customer service number, which usually connects to Mumbai it seems.
In any case, the agent can book your stay, and also email you a copy of the reservation. You can then use this to pick up your STPC voucher at SFO airport.
I have done this nearly 20x with no issues so far (fingers crossed).
I hope this helps.