Thanks for clearing it up, Larson Monkey; I searched for an Axis option inside the import options (hence my screen-shot) and even went back a few releases, just in case something would have changed.

The Axis Center's settings will be used for the Command "Center Axis To…".
To my understanding, it will not change the Instance object, but if you select "Use All Objects" in the Axis Center, it will affect the content of the Instance Object. I am not sure if that is the outcome you like to have. As the axis of the Instance Object is used then as an origin. I hope I got your question right. The Instance Object Axis manipulated by instanced points will change, but at that moment, move their content with them. So, if you use that Command again, the new position of the points, edges, or polygons will be used to position it. That can get messy.

From what I got, the All Object option in Axis Center will do that for you, but I'm unclear if the result will be to your liking.