Activate Tethering with ADB - Android 5.1
I'm uncertain behind the reason because I reached the result using trial and error but this command would do the job for Android 5.1.1:

service call connectivity 31 i32 1


As expected, you need root privileges. 

Also, you may be able to get something interesting from the source code of a service, in this case, it would be android.net.IConnectivityManager.