I just looked this up because I was interested. I lost a kitty in August (17.5 yrs) due to cancer, nothing to do with her being hyperthyroid. She was diagnosed at age 12 (most are diagnosed between 10-12) was controlled with medication. She was not my diabetic kitty I found this on the vetsulin web site so... hope it’s true & makes sense.
If your cat is hyperthyroid first, you will probably have started therapy and gotten the thyroid hormone levels near normal. Then if the cat then becomes diabetic, the hyperthyroidism (which is controlled) probably won't play a major role in the diabetes management.
The situation is a bit more complicated if the cat is diabetic, then becomes hyperthyroid too. Since hyperthyroidism has similar signs as diabetes (increased appetite, drinking, urination, and weight loss), a cat that is diabetic who continues to show these signs may be thought of as just needing additional diabetes management care. But the possibility of hyperthyroidism should not be overlooked. Since hyperthyroidism causes a general increase in the body's metabolic rate, it will have an effect on the diabetes and diabetes management. Often, a cat that is hyperthyroid requires higher doses of insulin in order to maintain the blood glucose levels near normal. As the hyperthyroidism is brought under control, the metabolism slows to a more normal rate, and the insulin dose needs to be adjusted. Pre-existing diabetes will probably have an effect on which hyperthyroid treatment option is used.
I’ll be interested to see if this is what others experienced.