When commanding Tibbers, he'll attack minions if they're in range, he'll attack turrets, but he won't attack the inhibitors or Nexus. It's been consistent across multiple games. He will attack any other objectives including dragon and Baron. (A note: I always use R to direct Tibbers. I have not tested if this changes if using ALT+click.)
Steps to replicate:
1. Summon Tibbers
2. Direct Tibbers to a turret; he will attack as soon as he is in range.
3. Direct Tibbers to an inhibitor or Nexus; he will not attack, but will attack minions if they come into range.