I eat fruit for breakfast every morning and have the opposite experience. I need to reduce my bolus.
My only thought is whether because you are eating less carbs, the dawn phenomenon is greater.
As for your no carb salad needing insulin, this is not unusual - when we eat no carb meals, our body breaks down the protein instead to get some energy. So, if I have a cheese omelette (just egg, cheese and a bit of olive oil), I will need some insulin,
There are some on the forum who have analysed their insulin needs with protein and can provide the insulin to protein ratio. I will leave them to comment rather than incorrectly remembering the ratio and misleading you.