There some variables here. Not every champion act the same way on every situation. It depends of many things and some of them you have to learn it by yourself.
Rhazin, for example, will start with his A3 on every Spider exept on spirit affinity, when he starts with his A2. That's the case when he is first or there are no debuffs on Spider.
Seer will start with her A3 when there is enough buffs on your and enemy turn or most likely will start with her A2.
Kymar starts always with A3, even there is no friendly skill to be resset.
Just some examples. How some champions may behave on auto is task, that lays on your shoulder. Even if you get some info from inet, there may be some specific, that is related only to your team composition.
For me setting up teams to play properly on auto in every content is part of the fun. Not fighting broken AI itself is fun, but overcome it. I play 9/10 battles on auto and almost never bother to switch on manual.