Hello,
I found these instructions from avast for installing the extension to safari browser:
Open the Passwords user interface.
Click Start now! to create your passwords vault.
Create your Master Password.
Install the Passwords extension in your browser(s).
Enable the extension in your browser(s) by following the on-screen instructions.
To set additional security options, click the status bar at the bottom of the screen or click Avast Passwords in the Menu bar on the top-left of the screen and select Preferences....
In my case there was not on-screen instructions. I have checked through Preferences that extension is active. Yet when I click the avast key icon there is a popup saying the "Avast passwords" "The extension is not activated". Avast Password software is running in the background.
Safari 10.0.3 OSX 10.12.3