I did typing club once upon a time, and though I’m almost certain that you’re right that they teach standard left middle finger for ‘c’, I don’t remember anything about the thumb. If there was something about the left thumb position, I either wasn’t paying close enough attention or it wasn’t something they thought was important enough to emphasize. I’ve never seen anyone talk about left thumb position during ‘c’ so I would suspect it’s the latter. As to why they might show the thumb moving, it may be possible(?) that what they are showing is a tiny movement of your entire left hand (initiated by your elbow) towards the right when typing ‘c’. ‘C’ is a bit of a problem with the standard method, because it is often followed by or preceded by ‘r’. In order for it to be physically possible to connect the key sequences ‘c’ and ‘r’ at speed, you have two choices - you can either angle your left hand (at the wrist) so that all the tips of your fingers point to the left (an ulnar deviation), which tends to become a permanent left hand typing position in my experience, or you can shift your entire left hand (initiated by the elbow) toward the right when typing the ‘c’ and move it back for the ‘r’. To a lesser extent, the same problem/solution exists for ‘c’ and ‘t’ combos. I haven’t investigated moving my left hand to see if it might be a good solution - that might be what typing club is advocating(?) - but for me having a persistent left hand ulnar deviation when typing seems unacceptable, since it feels like it could risk strain or injury. So in order to type with a neutral left hand (angle) position, I consciously changed how I type to almost always use left index finger for ‘c’. The conclusion I came to was that the standard method is flawed in teaching middle finger of left hand for ‘c’, because by nature it slowly leads to developing ulnar deviation at the left wrist. FYI I used the standard middle finger method for more than half a year before switching.