It's not that difficult actually. First of all, Torrent in itself is an unsecured p2p software. Instead of going through a particular server, Torrent links the individuals directly for the transfer of data. All the individual IPs are listed and logged by the Torrent client program itself. IP addresses can easily be tracked back to whichever ISP they belong to because ISPs are usually allocated a range of IP addresses they can use. You can use
www.apnic.net or
www.ripe.net to search for IP addresses too. In fact, some torrent clients can even log how much of a particular file a peer has downloaded (Whether this is coherent data or not, it's impossible to tell though).
What I'm guessing is BayTSP simply automates the logging and checking of IP address against the regional database. There's no hacking or breaking into private servers to obtain any information. They wouldn't know the identities of the torrents peers until they get the IP logs from the ISPs. I believe with most ISPs in Singapore, they are using dynamic IPs, which the ISP assigns to you only when you log on. However, as previously discussed on other forums, what this simply means is that the act of downloading is only associated with an IP address. This sometimes can be actually be quite a loose link.