This is perfectly normal. Fat has a tiny effect on blood sugars, and you probably won't need to inject insulin to cover it. Protein is a different story, especially in the absence of carbohydrate. The body can convert protein into glucose through a process called gluconeogenesis. It does this much more slowly than with carbohydrate, which is really good news for diabetics. Injected insulin cannot keep up with carbohydrate. You will almost always see a spike in blood sugars to begin with. However, injected insulin is much more suited to matching the absorption rate of protein.
Now the million pound question: how much to inject? Unfortunately it varies from person to person. As a guide, I inject 1 unit of fast acting insulin for every 20 grams of protein I eat.
In regards to your long acting insulin, you should not alter that to match your food intake. The idea of basal insulin is to keep your blood sugars stable throughout the day. If your basal dose is correct, if you were to go a day without eating or exercising, your blood sugars should not go into hypo or high levels.