The Newey bounce: How long did it take for his teams to succeed in F1?

On Tuesday, it was announced officially that Adrian Newey is joining Aston Martin. That will be the British master designer's fifth team in his career in the competition that dates back to 1988. Since then, other than with his first team, Leyton House, he has won a drivers' and a constructors' title with all of them. But how long did it take until the engineer could improve and succeed with his team?