Heres some of my personal observations from using the NPC:
All of this happened today while I was leveling my WHM/BLM (33/16).
-In order for your NPC to attack a mob, you HAVE to engage and attack with your weapon.
-If you get aggro, your NPC will not automatically fight the monster who aggro'd you.
-If you cast magic on the mob, like Blind, or Drain, etc, your NPC will not fight until you engage and attack physically.
-As soon as you disengage a mob and put your weapon away, your NPC will do the same and stop fighting.
-While fighting, I got a link at one point, but my NPC only stayed focused on the first monster I physically attacked. I did not try to switch targets because I wanted to finish one monster as quickly as possible before I died XD.
-I did in fact gain the option to change the NPC's job between healer, attacker, and shield types, after summoning it for the third time in three days.
-My NPC decided to leave after I gained around 600 exp. Since I was leveling WHM, this took a while to do, so my NPC lasted around 40 minutes. With that said, based on other people's information, the NPC might stay with you only until you've gotten a certain amount of exp. When mines left he said that "We have met our quota for today." or something along those lines.
Hope this info helps in some way :D