Imperial buff does not double item damage. This was patched in 9.14. Before the patch, items on champions with the Imperial buff will do double damage (e.g. ionic spark will do 400 true damage instead of 200).
The Imperial team synergy buff causes champions to do double damage. Before the 9.14 patch, this would cause items attached to a champion with the Imperial buff to do double damage. This was patched so that items are no longer affected by the Imperial buff.