The short answer is that you cannot do this, on an inserted IAM file, because (presumably) the part is a component of a subassembly that is instanced several times. Publisher currently works on the subassembly's "component definition" hence all instances are affected.
The only workaround is to export your Inventor assembly to DWF, and then insert the DWF file instead of the IAM. DWF does not have a concept of a "definition", hence does not behave this way (each subassembly is independent, even if identical).
The biggest (only?) downside of this workaround is that you cannot take advantage of Publisher's "update" mechanism.
As a separate point, note that you cannot explode a single part, only an assembly or selection-set containing multiple parts. The parts are exploded away from each other, so "of course" you cannot explode just one.
Jon Balgley