Seems like the setup is that the developer gets paid back via the market rate housing revenue, while the city gets a guarantee a minimum number of the new residences are rent controlled. So the developer self funds (or take loans) to start the project, it seems. And the city is still the landowner as far as I can tell, so the developer pays the city a share, which is how the city funds getting new office buildings for agencies to replace these.
I had to dig into what they mean by cross-subsidy to figure that out