Please keep in mind I have no major airline or Part 121 experience. Most of my experience is with helicopters, both military and Part 135.
I can't speak to Qantas' (or the repair station's) Tool Control program, but typically all boxes are shadowed.
If you take tools out of your box for line work, you would create a "mini inventory" of tools removed and placed into your tool bag.
If it's a tool room tool, you would exchange one of your tool chips for the tool.
If the tool was reported missing, there should have been a search until it was found. However, most tool control programs have a provision where the DOM can sign off that the tool was search for for a prescribed amount of time, unable to be found, and is presumed to not be on the aircraft in any critical areas.
Not all missing tools go reported due to fear of retribution. Not all tool control programs require a two-person signoff to close the tool box.
I don't know how big the "compressor turning tool" is for the A380's engine, but it feels like it should have been hard to miss...