I've added an event to my calendar locally on a phone. It was a meeting in the evening after my working hours. How am I surprised to realize that my stupid phone sync this event to exchange server and let this information publicly available to everyone on my work. How to disable such an updates? Local calendar should be local. I like how my phone download an information about ongoing events on my work and inform me but not vice versa.
Your "local and private" Android calendar is your Google calendar. When you've created that personal event it defaulted to your Exchange calendar. In order to avoid this is the future make sure that you create events in the calendar you want to. Usually it defaults to the last calendar you've created an event in.