I sketch out a song as maybe a 30s snippet in a DAW as if I was making a usual, non-generative track. Then I record a bunch of samples from VSTs I have. Once I have the samples I upload them to a server, which you request when you load up a song.
In your browser, the generators (which is another way of saying 'track') then piece together these samples in ways I have coded. So for example, I might have a list of chords which sound good, and a loop which selects from that set. Or maybe a bunch of note patterns to play at a certain interval, but they only have a small probability to play. To make it always unique (and hopefully always fairly interesting), I do things like automate filters, introduce randomness, and switch things around based on how long the track has been running for. Each track has it's own pre-defined set of samples and musical key. The code works on the arrangement, randomness and modulation over time. These random effects are different every play, and so each person will have a slightly different song than the next.