For sectors to act on their own you need to give them a focus and some resources. Sectors don't differentiate between energy and minerals; either one can be used for stuff.
Sectors on the balanced setting follow normal ai procedures: they build only when their is unemployment and they build resource buildings only when monthly resources are below a certain threshold:
/*First Priority*/
Minerals < 0
Energy < 8
Food < 12
/*Second Priority*/
Consumer Goods < 12
Alloys < 15
Amenities < 2
Housing < 3
/*Third priority*/
Everything else.
I'm not too sure on amenities and housing. Haven't seen the defines in some time. All the certain focuses do, as far as I can tell, is limit the choices for buildings.
Production builds only the resource boosters and hydroponic farms, as well as mines.
Manufacturing builds only alloys and consumer Goods as well as synthetic rares.
Research builds only research buildings.
Note, I haven't done a complete test, so do with this information what you will.
I've found that setting my colonies to balanced and just checking up on them every so often to be good enough. I typically like to micromanage the colonies before they become fully fledged planets so I can determine their first two buildings. I've noticed it's difficult for the ai to build Autocthon monuments and sometimes it gets stuck on a luxury buildings loop (it's because of the weights for the ai for it) so I manually build amenities buildings to resolve that. Sector AI doesn't seem to upgrade buildings or clear tile blockers, so be wary of that.
The ai is fine were it not for some strange ai weights found in the defines. Even with sectors set to automatic, I recommend you check your planets every so often to make sure they are doing what you want.