When Employee Calendars are set to Public, you can view it and have the capability to add an Event for that Employee. However, you are automatically being added into the Event itself so it will also appear in your Calendar.
In order to have the ability to create an Event for another Employee without being automatically invited to the Event, you can do the following:
1. Navigate to Activities > Setup > Calendar Preferences
2. Change Sharing from Public to Defined Below
3. Select the Employee you want to grant access to
4. Set Access Level to Edit or Full
5. Click Save for the changes to take effect
Repeat the same setup for all other Employees. With this, you can now create a new Event on another Employee's Calendar and you will not be automatically added to the attendee list.