Bag not cage (though the bag is technically a Faraday cage you aren't actually entering it as it's only big enough to hold your phone). A small faraday bag is available for ~20 on Amazon.
>They can do this at any time.
You can decide when you get updates and when you want to allow yourself to be tracked by whatever corporations, governments, and other actors that seek to track your movements. It's a false paradigm to suggest (like most people on this thread are doing) that you have no choice but to allow yourself to be tracked 24/7 or to go without a communication device. Keep your phone in a small shielded bag, remove it when you want to make calls, check your messages and are willing to divulge your location - its not rocket science.
Assuming the cage works perfectly (taking out the battery if possible seems a safer bet), the only thing you actually decide is when you get it out of the cage to use the device. However at that point the device can communicate and you cannot stop it from doing whatever it wants to. In other words: you decide you want to call, and if the thing decides it wants to update it might also do it at that point.