Why Registering ‘just’ a Utility Model Can Be Costly

When an employee inventor reports an invention to his employer in Germany, the rights to the invention go to the employer, who then has the duty to file a patent application for the invention. In return, the employee inventor has the right to be compensated by the employer.

But what if the employer files only a German utility model, which has a maximum runtime of 10 years (as opposed to 20 years for a patent)? Doesn't that deprive the employee of some of the compensation he is entitled to?
And what if he then drafts and files a patent application on his own? Can he claim compansation for that as well?
(Spoiler: Yes, it does and yes, he can.)