I used to work in law enforcement relations for a major cell phone provider. It is easy to not be detected: Use a burner phone. Regarding turning off your phone, that will probably do the trick, but if you are up to something so evil that the powers that be will pull out all the stops to track you, it’s probably best to use the burner.
But this is a great answer: https://www.quora.com/Is-it-true-that-the-location-of-turned-off-mobile-phones-can-still-be-tracked-if-the-battery-is-installed
Remove battery, wrap in tin foil, wrap that in towel, place into metal ammo box.
Yea, I'm gonna call BS on that article. I tried this a while back. Went out for the day to run my errands with my cell phone wrapped in heavy duty Aluminum foil, two layers. Told the wife to call and text every 20 minutes. The phone never rang.
Got home two hours later, unwrapped the phone, and nothing. No texts, no missed calls nothing. Asked the wife if it ever went to voicemail and she said no. Just a dead line, no ringing, nothing.
Just for good measure I checked on Google where it shows where your phone has been and nothing there either.
I would just check each phone and see if you get similar results. (or a better grade of foil :-)
Take the battery out.