By default, Day One entries may be indexed by the Mac Spotlight search service and included in the All My Files Finder view if you are using iCloud syncing or local storage of your entries. (Note: If your entries are indexed, they are only indexed locally on your machine.)
If you don't want entries to appear in Spotlight, follow these steps:
Locate your Day One journal in Finder. (Read: Where is the Day One data file stored?)
Open Mac System Preferences.
Drag the Journal_dayone folder (or Journal.dayone file if using Dropbox) into this window. (See image below.)