Pro players always make these little circular steps when fighting creeps. Why is that?
Honestly, this has nothing to do with auto attack on or off. Or standing still for that matter. You can be constantly moving, but not be applying the side step or animation canceling technique.
There are 2 main reasons why would you would do this side stepping as you would call it.
In both Dota and Dota 2, there is a mechanic called animation canceling. When your hero attacks a unit, the damage gets inflicted upon the unit before the animation is finished. So by side stepping really quickly, and then attacking again, you are able to cancel the ending of your first attack animation and then proceed to initiate another attack animation. This is widely used in the jungle as it increases the number of attacks you can deliver in a specific period of time.
Another reason to do this side stepping is positioning. For example, let’s say you are on radiant side, and at the bottom of a creep wave. But perhaps you want to be north of the creep wave and take an offensive position, while pushing the wave. The most efficient way to keep the pushing at a maximum is to hit a creep, animation cancel by taking a step forward and repeat.
EDIT: For melee heros, you side step after the damage is inflicted. For ranged heros, you side step after the projectile is released.