If I'm away from my computer for two minutes, the screen locks and a password is required. (Depending on circumstances, I may also use Fast User Switching to switch to the unpasswreded guest account) I fail to see how having to remember to close out Evernote every time I walk away from the computer is any more secure. However, we can argue this until the cows come home. Unless and until Evernote implements the feature you want, your option is to use a passcode on your computer.
Best of luck.