The komento component should have some module (comment module in this case) have a hidden token field with varied token value for different user.
Please try set komento component related module (comment module) to ESI module, then set the ESI Module Type to "private"
Thanks, I checked the komento component, it is using a plugin to generate comment area html souce code, our current cache plugin version do not support it. I will submit an update tomorrow to support this component tomorrow, thanks for your patient.
This version pass the test in my local site with the komento component you gave me, Can you email me your website information to firstname.lastname@example.org , it will be better if I can have a back end admin login account.