Some SPOILERS here:
Evolve red fungs so you can craft Cola (an instant cure for zombiton haywirefication). Stay out of their eyesight, cross water when they are chasing you, or stop moving (they only see movement). The small hammer stuns them but doesn't kill them. Blowing bubbles sooths zombs. Place their favorite dungeon tiles off to the side out of the way. Or evolve some carnivores!
I like the idea of tutorial tasks to help learn how to deal with the zombs!