Like I already explained:
a regular author in WP has in EME the right to edit his own events (the ones he created) or the ones he”s a contact person for. The contact person can be set per event.
View events in the backend is also limited like this.
If you want to limit events shown in the frontend, either use EME conditional tags with the #_IS_AUTHOR placeholder as check, or wait for the next release that allows this (from the changelog):
* Allow author or contact_person to be "#_MYSELF" if you want to limit events to only those where you're the author:
[eme_events author=#_MYSELF]
or the contactperson:
[eme_events contact_person=#_MYSELF]