Economics has always been a prime mover but other factors like wars can be a big motivator too. When many parts of Germany were devastated by wars and much of the population of some areas killed or driven off, immigrants from other countries, such as Switzerland where the population was growing, moved in to fill the voids. Sometimes religious persecution, such as the Huguenots in France, can cause people to move around.
In your case Martini may or may not originally been Italian. The name may have been Latinized at some point.