Ever since Horatio was confirmed as the headmaster of the Fifth Academy, he began using the methods from his past life on the prisoners: a small test every day, a major test every three days, the Basilisk supervising their studies, and anyone who failed got the Cruciatus Curse.
Thanks to his outstanding grades, Sirius Black was promoted to prefect of Azkaban Academy. As for Voldemort's diehard follower Bella, when Horatio slaughtered the pig containing Voldemort's soul and ate it as braised pork, she completely shut down. All one could say was that the Laughing Sisters had laughed until the very end—even Soothing Draught could not bring her back.
The other Death Eaters also became followers of Professor McGonagall under Horatio's high-pressure rule, because whenever Professor McGonagall came looking for Horatio, they got to relax a little. They now called themselves McNuggets, and their slogan was: "Being loyal to Voldemort is just for fun. For true greatness, look to Professor McGonagall! Loyalty!!!"
As for why Professor McGonagall kept coming to see Horatio? All that could be said was that Dumbledore, afraid Horatio might get too full of himself, had him continue attending classes with the other Gryffindor students as usual.
Then why did Horatio agree to Dumbledore's request? Because I wanted to pad the word count... Scratch that. Mainly, Horatio thought it was amusing. Just imagine it: when Snape called on Horatio in class, Horatio could say, "Watch how you speak to me. I'm the Azkaban Academy Headmaster, your equal in rank. The Slytherin Head is making things difficult for the Azkaban Headmaster. One hundred thousand points from Slytherin."
When Dumbledore came to Horatio and asked him to keep his prisoners in line, Horatio could righteously say, "Why should I manage them? I'm only a third-year Gryffindor student. I can't manage