just to inform, I have resolved the issue. It was caused by my xprivacy installation. My restrictions where to strong. Unfortunately I cannot reproduce, which settings I have changed in xprivacy to get it run. In case someone encounters the issues I had and also uses xprivacy, check the settings within “google contacts synchronising”. I think I have blocked the contact app to synchronise with the contacts provider.
All in all, DravDroid works as a charm. It’s also installed on my tablet (SM-T530, cyanogenmod 13, Android 6). I had no issues at all on the tablet (but also no xprivacy). I am really glad to have purchased DravDroid.