The problem is with how Joseph - the student - began his counterpoint...
...Aloysius - the teacher - explains that the counterpoint should have started on
Notice that Aloysius also say "the first misktake did not happen through any fault of yours..."
His meaning is that he didn't give Joseph all the rules before the assignment.
So for the mode to be correct it needs to start and end on the final (the tonic). Joseph's errors are marked with an
x above the notes, the notes I circled in red are Aloysius' (Fux's) corrections.
But some explanation of the text itself might be helpful.
The format in which the book is written - a dialog between a teacher and a student - is a kind of literary device meant to evoke the old Greek, Socratic dialogues. As a writing device I think the purpose was to draw the reader into the text, because you can kind of imagine being part of the discussion with the teacher. Perhaps you can imagine that you are Joseph the student.
The downside of learning counterpoint in this format is just what Aloysius apologizes for: the rules aren't outlined in a concise, logical manner at the beginning. As you continue reading be prepared for this. Lot's of rules will be explained after the failed attempt at the exercise!
Another way to think about this dialogue format is: we learn best from out mistakes. Writing Joseph's mistakes into the text embodies that idea.
As long as you know Joseph makes lots of mistakes and many of the figures in the text are purposeful bad examples the book is easier to read.