Another time money comes up is the episode, In the Cards, where Jake wants to buy a Willie Mays baseball card to cheer up his dad. He talks Nog into paying for it because as a Federation citizen Jake doesn't have any money.

I found some of the dialogue on Memory Alpha:

It's my money, Jake! If you want to bid at the auction, use your own money.

I'm Human, I don't have any money.

It's not my fault that your species decided to abandon currency-based economics in favor of some philosophy of self-enhancement.

Hey, watch it. There's nothing wrong with our philosophy. We work to better ourselves and the rest of Humanity.

What does that mean exactly?

It means… it means we don't need money!

Well, if you don't need money, then you certainly don't need mine!

I also imagine Starfleet officers in a non-Federation posting getting stipends. Or maybe Quark and other business owners bill the Federation for whatever Federation citizens buy? And maybe that arrangement doesn't extend to the auction with the baseball card?

There are references to Jake buying from some of the station's businesses. I think I remember him buying jom-jom sticks, and dining at the Klingon restaurant. (Did Jake ever use a holosuite on his own?) I'm thinking either Jake has some sort of allowance or stipend, and is exaggerating when he says he "doesn't have money", or those businesses make special arrangements for Federation citizens.