If you were on Gmail, and you wanted to communicate with someone on Yahoo Mail, you wouldn't try to log in on Yahoo with your Gmail account.
To interact with Kbin from Mastodon, you can either find the account or group directly such as @ernest, or if your server hasn't noticed it yet you can manually make your server notice it by copying and pasting the web address into the search box on your server.
The account @ernest is on Kbin, but you can interact and follow it