As Tobias said, wages in general only adjust in neighboring regions if people move between the regions until expected utility (of working in either region) equalizes. If there is a (fixed) cost of moving, people will not move until move until expected utility equalizes, but until the difference in expected utilities from moving in either region is equal to the utility cost of moving.
In the extreme, if some people just cannot move due to regulations, cost of moving would be infinite, and you could sustain any difference in expected utility.
Differences between wages and productivity
Why do I keep saying expected utility instead of wages? That is because wages in general reflect more than just productivity. They also contain compensating differentials.
That is, jobs have different non-monetary benefits (happiness you gain besides wages). To get a worker to do a job that is really not fun to do, you'd have to pay him more than for a different job.
This is a general concept. You have to compensate workers for working longer hours, under more strict bosses, having a more frictional labor market or higher unemployment risk, lower non-salary compensations, higher costs of living.
Some of these factors (and potentially many more) may speak towards German companies having to compensate their workers more - especially the cost of living.
This does not deny potential productivity differences
However, at the same time, you could really think that in a structured well-disciplined and efficient country such as Germany, companies get more out of their workers than elsewhere - meaning that their workers are more productive. Since it's not easy to measure productivity and it's causes at the firm level, I'm not sure whether this question has been addressed empirically.