Cancelling an extended warranty - how long does it take?

Hello, I recently bought a new car and got upsold on the extended warranty. The finance manager actually lied about certain features on the extended warranty (read the fine print afterwards), so I told them I wanted to cancel it. After some push back, they finally agreed to it, since in the contract it says I can within 30 days. They say it's been cancelled now but it will take a few weeks for it to show up at my bank (I financed the vehicle). Is it normal that it takes a few weeks to apply payment for something like this? I'm not sure if they're stalling for whatever reason, or if it actually takes several weeks for a payment to be processed. This dealership is pretty sneaky so I just want to cover all my bases

Thanks!