I currently have a profile set up for a warrior and heal bot priest that will do some damage.
My warrior profile:

//settings for global cooldown
gcd:1500

//auto attack
castspell:6603
distance<4
!autoattacking

//move into range if autoattacking is on but mob walks away
cast:20
distance<4
cooldown:5000
nogcd
rage<90

My warrior attacks a mob (thats right), and then my priest casts smite (thats right) but pulls aggro. If I'm auto-attacking, I won't move. However, if I manually turn off auto-attack, my character will move to the mob. Once again, manually press auto-attack and its fine.

Any thoughts?

The move closer action should work fine as it is, at least it does on my end. That is the whole profile? Did you make any changes to it without reassigning the profiles (use the grind button to (un)assign)?

there might have been something off, the assign/unassign seems to have made the difference.

randomly, the bot activating the second action bar. Any thoughts as to why?

Thats what the "fake" move closer action does.
The bot can't directly be told to move closer, but it will always try to meet a distance requirement of an action that has all other conditions fulfilled. And cast:20 means "press key 0 on bar 2", so it switches to that bar to do so. That key should be empty so nothing actually happens, except the bot moving to meet the distance<4.