I assume that you want to customize EPESI in such a way that a user (employee) will see only records (events) to which he/she was assigned. Is this correct?
First - when the record is created you can mark it public, public-read only or private.
For Contacts and Companies records - where you don't assign employees - if the record is marked as private by the creator of that record (owner) only this user will be able to access it.
For other records - where you can assign other users (employees) like calendar events, tasks, phone calls - situation is more complicated.
Imagine, that user A creates a meeting and assigns himself (A) and another user (B) to it. If he marks is as private than user B would not be able to see it, which defeats the purpose of assigning user B in the first place. Therefore EPESI checks who is assigned to the private record (let's say a meeting) and displays it on the calendar for both users A and B, even though it was created by user A and marked private. This is the only logical solution.
If you want to defeat the purpose of collaboration software - where all employees share information - instead creating an environment where you have one application but every employee keeps private data there - you can change it in:
Menu -> My Settings -> Control Panel -> Misc.
and change Default Records Permission from "public" (default) to "private"

Doing so "every man is for himself" (każdy sobie rzepkę skrobie) and this is the end of collboration as we see it, but it can be done.