yes, you have to switch on tracking. 

InReach devices have two kinds of tracking.  Log and Send.  Log is the locally recorded GPS track and Send is the Satellite tracking you have to have an active (paid) subscription to get.  The latter is pay as you go at the Safety service level.  You can control the periods of Log Tracking and Send Tracking independently including switching them off.  However they will not track (record)  if you do not start tracking.  There is a Auto track feature that will start tracking when you switch the InReach on.

Note: I have a Mini not an Explorer but I believe the InReach feature set is basically the same

I believe the Explorer+ has a barometric altimeter which must be calibrated but is more accurate than the GPS altitude.  I do not know if its values are tracked separately but I suspect they are combined with the log tracking.