They work just like they did in TOS, where everything is made up and the stardates don't matter.

For real tho. The TOS season 2 writer's bible (which you can find online) basically says the stardate number is a complex calculation that depends not only on time, but your location in the galaxy. I would not be surprised at all if the showrunners/writers are aware of this and are purposely doing it as an homage.