Google Drive provides 'Quick Access' feature which shows some files you edited or opened lately.
Well.. this could be useful, but if you want to prevent private files from being shown, you need to disable this Quick Access.
1) Click the gear icon in the top right corner and click 'Settings'.
2) Uncheck 'Make relevant files handy when you need them in Quick Access' item in 'General' tab.
In this way, you can keep your personal files from being exposed.