I spoke to Rabbi Mehlman last week, as he provides the hechsher for the New York DD (that have a hechsher). He said that about 2-3 years ago DD changed their procedure. They now ship the donuts (and other stuff) partially baked to each franchisee and each franchisee must finish baking it. Rabbi Mehlman said that DD franchisees without a hechsher can bake their kosher and non-kosher items together.
(He said it was better under the older system, as far as kashrus, for reasons I didn’t quite understand. He also said some DD franchisees still use the older system, but there is no way to know which are which offhand.)