Zombie Time has been discontinued or removed in the current version of the game.
Zombie Time is a type of Event and is automatically triggered for ten minutes at the start of every hour, only during Halloween though. During Zombie Time, darkness falls over Utopia and residents turn into zombies. Players collect candies instead of hearts during Zombie Time. Candies can be spent at Utopia HQ to complete Halloween missions. The event will stop triggering automatically every hour when the Abomination gene has been obtained and the Dark Tower has been built.
During Zombie Time, nine buildings are altered. Searching these buildings will uncover the nine body parts needed to complete the Ghost in the Machine mission and unlock evil professions. Evil professions* can only be spliced during Zombie Time. This event was added in version 1.60.
This event can also be triggered at the Dark Tower at the cost of hearts. If you don't have the Dark Tower yet, you can still trigger this event automatically at the Event Center at the cost of 25u.
note in order to get the dark tower you MUST find the nine body parts
and to get evil clones started do
Abomination and mutant will get you a evil clone and then you can bring darkness to your town
* The 1.93 update added the Rogue profession to the Evil category, but this profession is the only one which doesn't have to be spliced during the Zombie Time.