The way you want your zones to be set up is that when you enter one zone, all other zones are deactivated, therefore zombies will only spawn in the one you are in. In order to do this however, you have to set up adjacent (i.e., zones that are touching each other) zones in your mod's actual files. This, to my knowledge, is more complicated if you have teleporters and are moving between zones that are not adjacent to each other, but if you're doing normal adjacent zones, you shouldn't have a problem.
Just make sure that the spawners in the zone you want are targeted to the volume of that zone, i.e., the 'targetname' KVP of the spawner should have the same value as the 'target' KVP of the volume, and they should both follow the convention: <zone_name>_spawners. There are a couple other KVPs you'll need but in the video I link below you can see the whole process.
I highly recommend you check out
Jbird's tutorial on this, as it may help you out more than I did.
Hope I helped! Good luck!
