First I'll put in your original and then my re-write of it will follow so you can compare the speech between them. You'll see how I've made it a little more natural.

ORIGINAL
“But we need your help! My whole block is burning to the ground! Can't you put the fire out?”

“Maybe if you'd come here earlier today we could, but Hernando is hurt and needs medical attention. We're leaving immediately.”

Oumou was shocked. “But didn't you say when you came you would stay for the year?”

“That was contingent on the health and safety of our team, which is our first priority. I'm sorry about your block, Project. Good luck.”

With that, he got in the transport with the other People and flew away, leaving Oumou standing alone in the street. The feeling of dread had returned.

REWRITE
“But… you can’t leave! My whole block… it’s burning… to the ground!” She was nearly fainted from exhaustion and exasperation. “You have to help me!”

“Perhaps earlier we could have.” He spoke matter-of-factly, no sharing of her concern at all in his voice. “Hernando is hurt and needs medical attention so we must leave immediately.”

“But... you said you’d stay for a year.” Oumou was yelling through her shock at his disconcern.

“Yes, but that was contingent on the continued health and safety of our team; our first priority.” He hadn’t even looked at her, continuing to load his team onto the transport while he spoke. “I am sorry about your block, Project. Best of luck to you.”

Finished, he followed the others into the transport and flew away without looking back. Oumou was left alone on the street, left only with her feeling of dread which had returned.

Another comment, like Draugner said, is the continued use of Pods, People and Projects. Think about how you would refer to someone who was 'beneath' you. Would you continually call them a project, especially amongst your friends? The people more likely would have adapted a name for them; perhaps a PJT or something. Sure, Project would be the official name but the 'derogeratory' name that most People would use would be something else. The Projects would also have adapted a name for the People, something that shows their disdain for a group who believed themselves so far removed from the commoners. It's only natural among groups to do so, be them economic, social, racial, religious or whatnot. Especially in an environment where segregation is encouraged such as your story.

I like Draugner's idea of PASC but even that would become monotonous after a while. I would suggest giving the full name once in the beginning and then they refer to it as 'the center' in regular speech with the occasional full name or initials drop added in to remind the reader what 'the center' is.