Yes, children of illegal immigrants don't get German citizenship. One parent has to have lived here legally for at least 8 months or fulfill some other criteria, one of which explicitely deals with Turkey since the EU has an association agreement with Turkey that makes it easier to come to Germany for work or family.

You have to realise that the debate about illegal immigration and first/second generations is quite a bit different here for a few reasons:

last I heard there are "only" like 500k-1m illegal immigrants here

I can only find a report from 2009 without looking for ever, but there seem to be "only" 8-30k children with illegal status.

Public institutions for e.g. health and education are not allowed to inform the office for immigration about illegal immigrants.

The Schengen area, association agreements with e.g. Turkey and Ukraine and the large number of asylum seekers that Germany took in makes it kind of reasonable for a lot of important groups of people to immigrate.