Touch ID

According to Apple this Is how Touch ID works. My MacBook Pro does the same thing, it is fine

After you set up Touch ID, you can use it to unlock your Mac. Wake up your Mac by opening the lid, pressing a key, or tapping the trackpad. Then place your finger lightly on Touch ID to log in. 

You must type your password to log in after you start up, restart, or log out of your Mac. When you're logged in, you can quickly authenticate with Touch ID whenever you're asked for your password.

You can also use Touch ID to unlock these features on your Mac:

• Password-protected Notes
• The Passwords section in Safari preferences
• System Preferences 

If you are shutting down your MacBook Air it will ask for you to use your password. But if you log out or lock screen it will allow you to use your Touch ID

Hope this helps