He may feel more at ease with someone who projects confidence or he may be concerned that this is a part of your overall personality. His discussing his concern with the shadchan might be a way of attempting to find out more about your personality.
Frankly, I think it’s a mistake on the part of the shadchan to express it to you in a way that describes it as a negative rather than the inquiry being an attempt on his part to get to know you better.
She clearly hopes that her telling you will somehow influence your behavior on your next date. I think a comment that comes out like a criticism only serves to increase your anxiety about how you will be perceived on your next date (and, by the way, the right guy would probably be intrigued enough to continue to want to get to know you despite your anxiety, unless it’s excessive, in which case maybe the following will help):
My prior post was about the thoughts you are thinking and how they influence your behavior.
You might also want to try noticing what you do when you are anxious. Do you fidget, avoid eye contact, hold your breath, speak softly? Different people engage in different behaviors. When you can identify your own it will allow you to try to find alternative behaviors to counteract those habits.
I tend to hold my breath when I’m nervous, so I find being more aware of that and consciously taking slow deep breaths at least allows me to begin calming physically. I also “jabber on and on” so I have to really make a conscious effort to notice the other person. It can become a vicious cycle, where I talk when I’m nervous, notice the person I’m conversing with is very quiet (which might make me more nervous, because of my own internal self talk and doubts about myself, not the other person) and so I’ll talk on and on to fill the silence, only to exponentially increase my anxiety by just not tuning into my emotions and accepting them instead of trying to fix them. That is just an example from my life. You need to figure out what your behaviors are and what you typically do to “remedy” them that may not be working.