EDIT: Piet.t's surprising answer prompted me to delete and replace my previous answer. A quick google search indicates that he is correct.
13th Month Bonus Payment in Germany
Since your employees are on a
German payroll and subject to local employment laws, they may be
entitled to (or come to expect) a ‘13th month’ of salary as an annual
bonus. This amount should be calculated into the full year’s
compensation package before the assignment begins.
With that said, in the German courts, this issue may not be as clear cut as it seems:
The case was about an employee who had received a Christmas bonus
several years, but resigned in September, so he claimed 9/12 of the
bonus. The accused said : No, we only pay out when the employee is
still working for us on 31 december of that year. The first rulings
where in favor of the employer.
Based on those facts, the 10th senate of the Federal Labor Court ruled
in favor of the employee and granted him the proportional payment of
the Christmas bonus.
In any case, if you're not used to German work customs, you may want to argue that you didn't know about this practice, and therefore you may want to ask to renegotiate the original agreement.
After all, an agreement is a meeting of the minds. If each party had a different perception of the terms at stake, I think it should be worth pushing back a little on this issue.
Also, if you're coming from a neighboring country where your previous salary was 50.000,00 Euros and was paid on a 12-month schedule. It would stand to reason that you wouldn't want to move to a German company that pays the same salary but on a 13-month schedule. Doing so would be the equivalent of taking a pay cut.
So to compensate for the added inconvenience and added risk to yourself, you should ask that they slightly increase your total compensation package overall to make up for this.
And at the same time, you should continue to send out your resume and interview with other employers. Having other interviews lined up will give you more confidence to negotiate properly for yourself.