Hoffi wrote: That's how websites with sef/seo work.
I am quite sure the sef/seo doesn't work like changing a functioning link as "[mywebsite]/images/somepic.png" into a broken one as happened here "[mywebsite]/termine/event/images/somepic.png". I didn't experience these changes eg. on guttempler.de where both SEF and JEM are functioning without problem.
Yes, and that was because the article included a link to JEM "events of a single category" – which was added by RegularLab's plugin "Components Anywhere".
This has nothings to do with JEM, it's caused by the way you included the images. You must use "/images/..." instead of "images/..."
That helped as first aid – but still, I am wondering why guttempler.de and guttempler-duesseldorf.de are showing different behaviour although they use both same template, same general settings and same components. Whenever I might find out the reason, I keep you informed.