...how does the Detroit Locker know when to lock compared to an axle shaft speed difference of cornering?
Answer, it doesn't. It will lock all the time regardless of speed difference or direction of rotation whenever torque is applied. Only during coast does it allow for ratcheting and speed difference.
Detroit lockers are always locked. Sitting in their shipping boxes, in the carrier in your truck sitting in your driveway or driving down the road in a straight line they are spring loaded and locked. That said, what unlocks them is one axle shaft is forced to turn faster the the carrier. This forces the that side to unlock from the carrier. Imagine turning right in an Detroit equipped truck. The left side axle must turn faster has it goes around the corner. This action unlocks that axle. The truck is powered by the slower axle shaft which is turning at carrier speed. If the road is wet or snowy and you add enough power to spin that inner tire when it and the carrier reach the speed of the faster turning axle the locker will lock and with enough power to turn both turns the vehicle will spin both tires and you know what the result will be.
Think this out.
A truck equipped with a Detroit drives down the road with different diameter tires on the drive axle. The side with the smaller tire will be moving the truck. The other with the larger tire will remain unlocked even under applied power.
Clear as mud?
Applied torque to unlock the Detroit depends on where that torque comes from. Applied torque from the pinon, read applied engine power, will always lock the Detroit. If torque is applied by one of the axles, like turning a corner on pavement, will unlock the Detroit.
Did that make sense? Made sense when I was typing it!
Pretty good for typing on a keypad just a little bigger than a business card! Fat thumbs too!