That is one sweet job title. It also lets us know that our store owner's clientele are people who are separated from the place they'd most like to be: home.
while listening to the Puerto Ricans complain that it would be cheaper to fly to San Juan (10-11)
This is an exaggeration, of course, but—despite the complaining—the clients come to the store as way to revisit their homeland. Buying the coffee that you used to drink there, even if it's overpriced, is the next best thing to a plane ticket home.
and to Cubans perfecting their speech of a "glorious return" to Havana (13-14)
The fact that the Cubans are "perfecting their speech" suggests that they've been practicing—notecards, PowerPoint, the works. The idea of home is so alluring that they seem to be revisiting it through their rehearsing.
all wanting the comfort of spoken Spanish, to gaze upon the family portrait of her plain wide face (18-20)
How can one face look like a "family portrait"? This isn't some Picasso-inspired cubist commentary. Instead, our store owner is a familiar face. She reminds her customers of the people they have left behind to come to the U.S. That's one reason why they now feel so at home in her deli.