How is reserve money 'multiplied' by the banking system?
This overlaps an existing question: Can money multiplier happen within a single bank? The mechanics is described in there, and I think it addresses some of your questions.
My guess as to what is happening in the explanation you found is that there is an added behavioural assumption: banks only make loans up to the size of their excess reserve position. This means that if there is an injection of reserves, there can only be a loan of the same size as the injection, then a sequence of smaller loans. You then end up with diagram result. The reality is that this is not how banks operate, and they could just make a single loan and use up the excess reserves in one shot. (Obviously, could be done in smaller steps.)
The “sequence of small loans” story was probably in an old Economics 101 textbook, and it has been repeated many times. I have not seen a formal version of this model, so I have no idea why the non-existent constraint on loan size is imposed in the money multiplier model explanation.