Gave a structured answer describing the Situation, The task, the Action and Result. They want to see how you tick under pressure, so utilise experience of dealing with people, and being structured and organised how you approach the situation
If budget or targets are being changed mid project and frequently enough that they are asking about it mid project thats a massive warning sign that they do not set projects up properly in the first place. Not somewhere i would want to work.
I said that I am flexible and adapt quickly to all styles based on companies preferences and thrive on feedback however if I am to name my preferred style that would be chain management over micro management due to lack of mutual trust between employer and employee.