Assuming that you are well prepared and crack your cases, then confidence won't come with further refining your case skills but will come with more practice of full interviews. By agreeing upfront with your interviewer to give you specific feedback on this dimension in upcoming practices you can address the verbal and non-verbal cues that make you come across as insecure.
In the past, when I gave the same feedback to interviewees it was because I could tell they were more worried about the interview outcome and about giving me the answer they believed I wanted to hear vs. being concerned about the case at hand itself and find joy and satisfaction in solving it. That also showed in fit questions where instead of being excited of sharing a personal experience to answer my question, they seemed focused on weighting carefully the words they were using.
My recommendation (and I am aware it's extremely hard to put in practice) is to try to enjoy the interview as much as you can by focusing on the challenge of solving the case and the satisfaction it brings you when you solve it and the joy of sharing your life experiences with someone else. If you are able to do focus on these aspects, and not think and care for those 45 minutes about what is at stake, then (usually) you will come across as genuine and confident.
Hope it helps,