ADF works for a lot of people, so if you are doing ADF on a prolonged basis and you are not eating two days worth of food on your non-fast day, then yes you do burn fat. For one day of fasting taken on its own you may or may not lose weight depending on what you ate before fasting. Probably depends on how much glucose and glycogen you have in your system, food remaining to be digested, and level of serum insulin.
I don’t know how closely correlated urine keto is with losing fat, especially in the early stage of a fast. Probably the best way to check this out is just record your weight at the same time each day over a couple weeks. I do 4/7 weekly fasting lately and I record my weight when I wake up each morning and it is a clear indication of weight loss - about 2 - 2.5 lbs a week.