Correct, low intensity cardio is best for fat-burning. The reason is quite simple.
Your body cannot break down the fat molecules and use them for energy quick enough for high-intensity exercise such as flat-out running and anaerobic exercise such as heavy, moderate-paced lifting. So instead of pulling from fat reserves, the body actually pulls from glucose reserves for HIT purposes. In fact, the body cannot pull from fat energy in high intensity and anaerobic exercise.
If the exercise is slow and steady and therefore much less demanding of energy, the body can use fat cells as it's primary source of energy during such. Granted, it can pull from either glucose or fat but this is why I said to train low-intensity after heavy lifting so that your glucose levels are rather low. Otherwise train in the morning before eating, where again the glucose levels are low. It is also important to note that when you lift weights, your body secretes more testosterone, epinephrine and T3 to metabolize fat molecules. This process takes 30-60 minutes to take it's full effect which is another good reason to consider cardio after weight training.
I'll go ahead and explain briefly why carb cutting is a big no no in bodybuilding. As you can imagine, we need plenty of carbs for the HIT stuff like weight-lifting and circuit training of the sort since our body cannot resort to fat for fuel during this type of exercise. But we also need little to no carbs remaining in the system for cardio in order to pull from fat reserves exclusively. When you cut your carbs, you actually aren't providing greater opportunity for fat burning. Sure, you'll lose weight - just not good weight. If you cut carbs, expect to lose 1 pound of muscle for every 2 total pounds of weight. This is why people generally get weaker on keto and carb-cycling diets. I'd also mention that not only are they catabolic to the skeletal muscles but also the heart, which is dangerous. You should never need less than 1g of carbs per lb of body weight - period. If those carbs are clean, this is more than enough carb cutting to maintain most of your muscle and still effectively burn fat. Honestly, if you have the timing and diet correct, you can bulk and cut simultaneously by targeting fat cell usage at certain times during the day while still eating enough carbs to adequately provide the constant fuel the muscles require. Don't believe me? I've been cutting for 3 weeks now while eating 300+g of carbs every day with my 175g of protein. Granted, I eat very little dietary fats but I replace them with MCT. Anyways, I've gotten leaner and heavier.
Dieticians never bothered to tell online forums why we should cut carbs or increase carbs depending on our goals. We do all of this to manipulate the insulin to glucagon ratio, which determines everything when it comes to whether or not you build muscle or lose fat. That ratio should change depending on the goal of fat loss or muscle building. Protein and carb intake has a direct relationship with the ratio, so as you can imagine eating a certain ratio of carbs vs. protein can easily put us where we need to be.
Hope this helps. I long-winded. I know.
Also, I understand that alot of people on this board do not agree with half the statements above. I can easily find documented studies indicated such results. There are also tons of other sources that explain the metabolic science of the body which you will find is congruent with what I am saying here.