Enemy spawning in Objective Mode is very different than it is in Wave Mode. Adding zombie volumes to an Objective Mode map will not automatically cause enemies to spawn when the map loads like they do in Wave Mode. In order to make enemies spawn you need to do abit more work, but it'll be worth it in the end because you'll have total control over what gets spawned and when!
Before you can get an enemy to spawn you need to create a 'squad' for it. Squads contain information about the number and type of enemies that should spawn in a particular group. You could have a squad with only a single enemy in it, or a squad with dozens of enemies, it's up to you. To begin creating squads you must first place a 'KF_StorySquadDesigner' actor somewhere in your map. You can find the Squad Designer in the actor classes browser under Info -->KF_StorySquadDesigner
Once the Squad designer has been placed you should select it and press F4 to open up its properties. You will notice that it has an empty array called 'Squads'. Click on this and select 'Add' to create a new entry.
Naming your Squad
Now you should enter a name for your squad. A common convention in Tripwire maps is to name enemy squads after objectives followed by a letter to differentiate them. i.e "GoldBarSquadA". This is helpful because it reminds us which objective these enemies should be spawning for. But really you can call your squad whatever you want as long as it's not a name that has already been used somewhere else.
Adding ZED types
The next step is to click 'Add' next to Squad_ZEDs. This will add a single type of enemy to your newly created squad. The 'NumToSpawn' value indicates how many of that type of ZED should spawn in your squad. You can add as many different types of ZEDs as you like, including custom ones (if you are making a mod that has it's own enemy type). To do this simply set the 'ZEDType' to "ZED_CUSTOM" and select your custom enemy class from the CustomZEDClass dropdown. The squad pictured below would be comprised of a total of 5 ZEDS - two clots and 3 crawlers.
Creating a Wave
Adding a Wave Designer
Now that you have created a squad it's time to set up a wave that will spawn them. To do this you must place a 'KF_StoryWaveDesigner' actor somewhere in your map. You can find the Wave Designer in the actor classes browser under Info -->KF_StoryWaveDesigner. It is usually a good idea to place your wave designer next to your squad designer, so that if you have maps with multiple wave / squad setups you can see which ones are grouped at a glance.