In order for a Bluetooth device to work with smartlock, it needs to be constantly connected while it's within range of your phone. Dedicated smart watches, Bluetooth speakers, and your cars Bluetooth are constantly connected to your phone to pass data (calls, texts, music, notifications). For a lack of better term, the Bluetooth connectivity is "active" (always connected) for these devices.
Fitbit on the other hand only connects periodically and only for a few seconds to sync health data. So basically Bluetooth connectivity is in "sleep" mode (disconnected) until the timer activates Bluetooth to sync health data and then disconnects again after it's done.
There is an option for your fitbit device to notify you of incoming calls, however this still doesn't maintain Bluetooth connectivity. When you get a call, your phone temporarily activates Bluetooth to send the signal and then disconnects. This is why your fitbit gets a delayed notification instead of an instant notification like a true smart watch which has permanent Bluetooth connectivity.