Back in the 80s an entrepreneur here in Florida opened a little ice cream store called " Twistee Treats ". He then went on to open several more. His stores were unusual because the buildings were pre fabricated and trucked to the location and then assembled. The building was a replica of an ice cream cone and was just big enough to hold two employees, ice cream and a walk up window. They placed them in shopping center parking lots or where ever they could get a spot. The first model I ever photographed did their TV commercial
I'm not saying that's where " Twistys " the website, got it's name as that's something Shap has to answer but that's the first time I heard " Twistyee " and " Treat " used together.
http://www.agilitynut.com/food/twistee.html