With Matthews, it sounds like they used a tendon that attaches near the thumb, and has another attachment up the arm. Disconnect up the arm, turn it around and anchor it on the broken thumb to generate strength (this seems extreme, weird and unlikely). More likely, they moved a tendon from the neighboring finger (which has two) and anchored that. The hole they drill is probably to allow the thing to get to the other side to anchor so it's stronger (they do this in ACL surgery) - or to get the proper movement of the thumb when the muscle attached to the tendon fires. I'll ask someone who's actually done this to illuminate...

The weird thing is that after tendon transfer you have to retrain your mind to work the thumb by thinking about extending your index finger, I believe (assuming it is the extensor tendon that was transferred).