It is not possible for the add-on to know whether or not you are successfully logged in to a particular website (This is actually not a limitation of Password Depot but is basically technically impossible).
This can lead to unwanted effects: Even though you are already logged in the add-on tries to fill in more fields on the website.
This problem can be solved by limiting the login URL to exactly the URL where the login takes place.
To do this, delete the template used, which could look as follows:
Replace then the Default URL with the exact value as shown here: