Hello,
i understand the app in the following way:
if i want to use it on my phone and my tablet, i have to create an account (trakt or tmdb). So i have a tmdb account. Now i can see my personal lists on both devices. But i can’t save movies on my lists anymore. If i work as a guest, i can click to the right of the icons 
and watchlist (the bookmark icon). If i’m locked in with my tmdb account, the icon to save in a personal list disappear. Have i missed something ?
Hi, for sync your data you can use Trakt or TMDb. TMDb doesn’t support all features at the moment. For example watched items or adding personal lists aren’t in Moviebase integrated.
I recommend trakt if you want use all features without limitation.