The Krebs cycle does go continuously. You're burning fat reading this post. When you exercise, you burn more fat via the Krebs cycle. Fat is burned preferentially to amino acids because fat is easier to convert to energy. Obviously, I'm keeping this simple. Detailed info can be had via an internet search, I'm sure.

When does it kick in - it starts running fast & burning more fat after the easily burned sugars are gone (again, I'm keeping this simple.) A lot depends on your body, how much sugar is stored & how quickly your body starts using fat for energy.

Rather than getting entangled in biochemical stuff, the most important things I tell people are: It's calories in vs calories out and most people overestimate the calories out part & underestimate the calories in part. This is a lifestyle change, not a quick diet. Exercise moderately and do it often - keeps your metabolism running higher. When you're done exercising, you should feel like you still have a little more in the tank. Diet is the most important part. One doughnut can wipe out half an hour on the treadmill.