I'm more bothered by how the tadpole could be infecting him—like how does it even work?
Because the tadpole is not a biological parasite, it literally consumes your consciousness and your soul, your body is merely a vessel for an illithid consciousness, that is quite probably poured into you by an overmind.
Imagine a tadpole like an antenna, it hooks itself onto your brain stem and waits for the signal from the overmind. When the signal arrives, the overmind uploads a unit of illithid consciousness to the tadpole and the tadpole transforms the body to reflect the consciousness of a mindflayer. It might sound like a bit of a reach until you realize that the mindflayers can build flesh-airships with psionics. Compared to that, transforming a mere body, even if it's undead, is nothing.
This also fits into the way mindflayers feed. They don't actually need the brain, they merely eat the brain for the psychic potentials it contains, memories, etc.