According to Wikipedia, they didn't. The big Mennonite emigrations out of Germany started in the 1600s, due to religious persecution. Anabaptism was made punishable by death on the Diet of Speyer in 1529, and the only thing that saved the Mennonites from extinction is that they did not call themselves anabaptists. read more
There were small waves of Mennonites that came in the early 1800’s they were Swiss. I don’t know of any other significant waves of Mennonites that late in history, but if your family came in the 1800’s and they were Mennonites, they might have been Swiss. Check this out, Stoner Ancestors Or they were converted by their “Master”. read more
By 1759 a few Amish began to move into Lancaster County where many Mennonites lived. A letter written in 1773 by Mennonite bishops stated that the Amish "hold very fast to the outward and ancient customs." The German Pietists Mennonites and Amish made up only about 5000 of the German immigrants. Most Germans immigrants were Pietists. read more
The term "Russian Mennonite" refers to the country where they resided after their emigration from Germany and not to their ethnic heritage. In 2014 there are several hundred thousand Russian Mennonites: about 200,000 in Germany, 100,000 in Mexico, 70,000 in Bolivia, 40,000 in Paraguay, 10,000 in Belize and tens of thousands in Canada and the US and a few thousand in Argentina, Uruguay and Brazil. read more