This is exactly what happened to me--even on a PAID ticket (bought at ual.bomb BEFORE the schedule change(!)), I spent hours trying to figure out who was responsible for paying for the hotel. SQ will tell you that if your "travel agent" (UA) "requests" for the hotel (i.e., pays), then it can be done, but since UA is your "travel agent", if you call UA, their agents (unless you're 1K) will not help you. Period. You will know MUCH more than they do about the topic. Possibly mentioning the term STPC will help get you somewhere, but it's not likely. Ask for a supervisor right away, but I'm guessing they'll tell you it's an award ticket, so no dice. Then I'd go back to SQ, and at last resort, I'd ask the CGK Station manager when you check in. According to SQ, the only one that can request this STPC is the station you depart from, which is CGK.....
Maybe your luck will be better than mine, but on an award ticket, you should be in for at least a bit of a run-around!
If you note above, my outbound (PEK-BKK-SIN-CMB) was a BMI *A Award ticket, and it ended up getting paid for by SQ, but only after plenty of questions. In fact, it wasn't a done deal until the door closed in BKK (my last station of departure before the STPC) and I was on my way to SIN that I was assured of a hotel in SIN. Everything worked out, but it's not nearly as simple as it sounds.
Enjoy, and be sure to let us know if you have an easier time of it than I did!