There is 2 types of carriers. Government, such as USPS and Hong Kong Post), and Private (such as DHL, Fedex and UPS). If the government postal systems agree to it, they ship in conjunction with each other. HKP and USPS both have similar enough guidelines to work with each other. So you could go to your local post office and mail something to Hong Kong and USPS will just forward it to HKP. Since USPS doesn't go to individual businesses or residences in Hong Kong, the USPS options first goes through HKP. This is recommended because it is usually the fastest and cheapest way to deliver a parcel or letter.
How did yours end up in Singapore Post? Depends on when and what was shipped. fasttech, as near as I can tell, has a channel straight to Singapore which bypasses Hong Kong customs and makes it to USPS through Singapore. fasttech decides, according to what you ordered and what is happening in Hong Kong, which is better for your order if you choose USPS.
I don't think SP actually transits through Singapore, I think it goes through the SP offices in HK and then out to the destination country. They both pass through HK customs, that's why FT is switching batteries to China Post which must go direct from the Chinese mainland at a guess.