Follow these steps to make your events private:
Google Calendar --> Settings --> Choose the calendar under Settings for my calendars --> Access permissions for events
Make sure those are set as "See only free/busy (hide details)"
Have in mind, that if you're the one hovering over yourself in Teemyco, you will always see the event that is coming up.
But if the settings are set as private, the other people won't see the same thing you see. They'll see "private".