This is not an issue with Face ID, and is is no bug.
EN works like this on devices with touch ID as well. Once the device itself is unlocked, EN is open for use until the device is locked, or locks itself (timeout).
For iOS apps, this is the standard behavior. I have few apps that expect an authorization every time I open or come back to them. These are banking apps, my password manager, authentication apps etc. I would not like to have Evernote restricted like this, because it is a work environment. Remember, there are many devices running iOS without Face ID.
If you want to make access more restricted for your usecase, you can set a passcode in settings of the iOS EN app, and define that it is needed every time you (re-)open the app.