You must understand the difference between motor and sensory nerves.
The former stimulate muscles to move and botox works and the interface between nerves and muscles to prevent the signal to contract from working. The actual goal is paresis (weakness) or paralysis (cessation of muscle activity).
The other set of nerves allow you to feel pain, vibration, temperature, etc. The tingling is most likely that the sensory nerves may have been injected. Generally this resolves within 3 weeks after injection

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