I would consider it his problem. The one I see has gotten snarky a few times when I had to correct her about her role in my life - a couple of time she has said things like "god forbid I should feel good about my job" and I usually simply stated it was not my place to try to make her feel good about her job. I didn't really see it as insecure - more just not my problem. The woman does not really say anything about the second one I see anymore. She usually only said it was my right if I wanted to see another one and once commented I must spend a fortune on therapy. I just said how much I spend is my problem not hers and as long as her bill was paid, there was no reason for her to concern herself with it.
She also once tried fishing to see if I would tell her if I said anything about her to the other one and I informed her I did not spend money talking about her to the other therapist.