I can't imagine they make much of a profit as the DLC itself seems rather costly to create.
I mean for a new im@s song that means they have to hire the dancers, set up the 3D rigs, get every voice actress to record the song (and it doesn't always happen in one take).
The DLC might be just a way to extend the game's playability while the developers work on the next big thing in the iDOLM@STER franchise and is a way for them to make a little spare change while doing so.
I imagine everyone involved is on a contract guaranteeing at least X amount of catalogs, but that's just my conjecture. That way, everything is paid for up front, and you know you'll make everything by Y date, or someone gets burned bad.
Also, intuitively both Sony and NBGI would get a cut of the profits (how it's split, dunno), 'cause otherwise you'd be selling stuff to Sony and not the users. I mean, if Sony bought the DLC then in turn sold it, the developer's one step away from the consumers, and I'd imagine that wouldn't pan out too well for the consumers in the end. Me, I'd imagine that you'd pay for space on the PS Store, whether it's advertisement space or the rights to even be listed, and Sony takes a cut on top of all your sales. There was actually some conflict between Microsoft and some developers about this, since some developers (who were also the publishers) wanted to release content for free, but MS wouldn't let them 'cause then guess who didn't get a cut?
Though buying a Japanese game's Japanese DLC in the hopes of getting it localized... well, if they can actually pinpoint that the person buying it came from the States or something, sure. Don't think they can, though.