Hi there,
first of all: Thank you a lot @thomaso & @postmadesign.
You're answers helped me, because I already doubted myself.
@postmadesign : Your idea sounds absolutely reasonable. I already tried this (setting the document as well as the color setting to CMYK) – but my printing shop still insists, that it is RGB anyway.
@thomaso : I will try that "PDF/X1a" thing, for sure.
All in all it seems to me, that it SHOULD be working, but it doesn't. As it is a "beta" I'm fine with it, but really hoping, that the "store version" will be able to handle this whole RGB/CMYK-thing properly. Would be a shame if it wouldn't.