Where do you have the email account set up? In Notification Center or in your personal settings? They are different. And in personal settings make sure that your mail connection works.
That might be a good thing LOL.
You may want to ensure that it actually gives you a REAL benefit if enabled and that you know how to recover if/when it doesn’t work. There are many posts about issues getting in, particularly if the email stops working for one of a million reasons.
There are many better ways to protect your NAS, in most cases, such as running secure VPN access on your router. Do you really need an authenticator app? Yet another spp that you have no control over and give access to your credentials/data.
I’m not saying this isn’t appropriate in your situation, but beware there are drawbacks to it as well, and you should read about it first, then see if it is something you really want to do.
Including basic information in your post such as NAS model and exact firmware version can also be critical to get the answers you need.