I know this is an older thread but a Mini Jersey is a Jersey (not crossed with another breed) that is under 42" tall I think. As far as I know you do not breed a Jersey to a Dexter to get a Mini-Jersey. Mid-sized Jerseys are between 42" and 46" tall.
Yes, you are right. They are the breeds crossed with Dexture, Lowline Angus, Galloway, possibly even Zebu etc to get a better yield out of the cows. And for getting the better quality and quantity of milk this kind of breeds are crossed. When breeding the miniature Jerseys one must consider that not all the calves produced will remain in the miniature size ranges, even if two miniatures are bred together.