There are no legitimate indications that the body reacts to sweetness in any such way except from junk scientists who are more interested in grant money than they are in the truth.
Insulin facilitates the metabolism of carbohydrates. Diet Coke, with aspartame, contains 0% carbohydrates. It provides 0 calories. How do you stimulate insulin without calories?
This is just more nonsense from people who don't understand the chemistry of satiation. Suggesting that the taste function can control or influence the amount of calories that go into our bodies is absurd. This is not how the body is set up and contradicts what we've learned about hunger and satiation. These people seem to believe that the body's genetic structure can be overridden.
You might find this interesting. These folks are solid researchers and are not driven by ulterior motives.
* In this study, Perrigue compared subjects' level of fullness (satiety) after consuming high fructose corn syrup (HFCS)-, sucrose- and aspartame-sweetened beverages with milk and a no-beverage control. The study found that all four caloric beverages "suppressed hunger ratings and increased satiety ratings relative to the no beverage control. However, there were no significant differences in satiety profiles among the sucrose- and HFCS-sweetened beverages, diet cola, and 1% milk."
It's from a pay site so I cannot link you. You can find it in Nutrition Today: Volume 40(6) November/December 2005 pp 253-256 by: Gayle L. Hein, BS, and Maureen L. Storey, PhD, Center for Food, Nutrition, and Agriculture Policy, University of Maryland-College Park, College Park, MD.
The internet is filled with so much misinformation based on junk science that you really need to be careful as what conclusions you believe.