AS350B3e Starts when Bat turned on  

 could be starter switch or starter relay , I have had the oppposite of where I couldnt shut down . There are two relays that are same and your mechanic can swap them to trouble shoot.. please let us know what he found . I am like you , I know most just leave it to maint but I too like to find out if others have had similar problems which can be very helpful to your mechanic especially if he is new to airframe or industry , which is not unusual in our line of work, plus good mechanics like it when you show interest in their profession , not to be a critic just curiosity.