The International models have a spring loaded, trigger fired, extractor, that fires the empty out and you have no real say in the amount of effort that it puts in.
Essentially, the block coming down hits a trigger/sear unit that 'fires' the extractor.
The block closing, re-cocks the mechanism.
The International models have almost NOTHING in common with the regular BSA Martini Actions!
I must admit, I mixed up the Model 12 MkII International, which I never owned, with a couple of BSA Model 12/15 match rifles I owned.
Your description really got me curious so I looked up the Model 12 International to look at its operating mechanism. They do have very aggressive extraction and fling the empties.