I would expect anxious/insecure parents to use placating behaviours (like device use) themselves, and I would expect their children to be anxious/insecure too.
So I would expect the study to find that the children of phone-overusers were more likely to be anxious/insecure.
Still, I would also expect that less phone use (subbed with more attention to kid) would help the kid with this.
I can easily imagine the phone use and the kid's insecurity both coming from the same underlying family dynamic, rather than one neatly causing the other