To use the same functionality as the property palette does, you use the ActiveX Move method (i.e. vla-Move). You could also use the move command to accomplish the same task. I can't remember if modifying the ActiveX Position property does the same as the Move method or as the entmod function. Too long since I've worked in anger in AutoCAD, never mind AutoLisp.
The reason this happens is because of how AutoCAD saves attributes. They're actually separate entities, just grouped with the block by being those following it and ending with a SEQEND entity. So editing the INSERT entity does not affect the attributes. If you want to stick with using entmod, then you need to modify the ATTRIB entities following the INSERT in the same way.