So by using Chipmixer, does it change the private key instantly? The fear/question has always been, if someone finds the key to #64 and moves it, someone can use the kangaroo and solve it within seconds and gain the private key and give higher trans fee and move it to their own wallet. Make sense?
No. The way it works is that you send all the balance to the deposit address, thereby emptying the private key. Of course, you should use a high transaction fee to reduce the chance that somebody can start and finish Kangaroo before the transaction is confirmed.
Once the transaction is confirmed then Chipmixer is holding the money at that point. It cannot be taken by a hacker. You then follow the instructions on their site to split up the balance into multiple outputs of different sizes such as 0.001, 0.002, 0.004, etc.
Then you let it do it's mixing activity (which the hackers can't track) and it will send all of the outputs to a private key they created. They will then give you the private keys to import into a wallet. If you don't trust them though you can always move the coins to a second address you have created, and that's private because hackers don't know the private keys you imported in the first place.