Well I think he will be kept on due to the teams performances ( not results) and for winning the cup. No point sacking a manager after a year after letting him build a team. Took man city more 1 year and 100 m to get where they are.
Does that go some way to answering your question?
Man City also showed progress in the league each year after they spent money. After they were bought they went from 10th, 5th, 3rd, and now 1st.