Singapore is online visa application. Upload all the required documents as listed, then if it's accepted, you go and turn in the paperwork and passport. I believe it is then next day collection.
At this time, I wouldn't apply and not be able to supply the required documents as listed. We are seeing this in another thread.
The person you spoke to on the phone is likely not to be the same person dealing with the application. Hence they won't give names and put themselves in the frame.