Carbohydrates and protein raise insulin with protein having about 1/2 the effect, but it is often overlooked that fat also raises insulin to a small degree, what doesn’t seem to be known is how variable that effect can be and whether or not it is something else in the butter that can be affecting it besides the fat since butter is still dairy.
Personally, I think the effect of 1 to 2 tablespoons of butter on insulin is probably not the issue, but it is possible, especially when people start melting entire sticks of butter in their coffee. For you, more than likely it is something else in the butter, so you might try ghee (clarified butter) instead as a test.
Personally, I don’t like ghee and use coconut oil and/or MCT oil instead of butter when I’m having a fatty coffee to get me through a low-energy period.