The question explains itself. Will other cities in my region produce money, oil etc. while building another city in the same region?
No. City simulation is entirely client side as stated in this Rock Paper Shotgun interview.
The servers are not handling any of the computation done to simulate the city you are playing. They are still acting as servers, doing some amount of computation to route messages of various types between both players and cities. As well, they’re doing cloud storage of save games, interfacing with Origin, and all of that. But for the game itself? No, they’re not doing anything.