Yes, magic comes from life. Background count itself generally comes from emotion and aspected power, however. Nobody has decided (or can, for that matter, until someone officially writes them up) 'hey, each of these is a walking mana ebb or background count,' so I'd assume they don't pack around their own zone as a result of being undead. In fact, you could argue that a possible cause for all these undead is due to the planet throwing up some anti-human 'anti-bodies' to fight the infestation.
That doesn't mean they won't have a background count related to having been a metahuman who was attacked and killed by zombies; if I remember right, the current rules have a... +3 background count spike at a 'normal' murder scene for a few hours? (Though I personally dislike that as it makes background count far too... Fluid, for my tastes.) So 'fresh' zombies would be a pain in the ass to magic users for sure. And any place where lots of people died would have the background count linger, perhaps forever (or at least 'forever' as far as the zombie apocalypse survivor are concerned).
Throwing a constant background count everywhere it matters (i.e. on almost every enemy) is a bit of a dick move to any magic users in the party.
Also, shaitan? You mean shedim? The extra-planar entities whose entire purpose and goal is to exterminate all life everywhere, and do so merely by standing around, much less before they apply their malign, alien intellect to making it happen faster? With a seething hatred for all forms of life?
And Techno-zombies? You mean CFD? Or Cyber-zombies, which are a very different thing, both of which are very different from zombies.
There's specific terms for these things for a reason.