Setting up a last gen model, not the current model TC - should be the same as I am using the most current version of Airport Utility for the setup.
On the TC,
I have file sharing turned on,
I am using the same password for the wifi network and the TC - you would want to use a different password for each.
Two Macs with 200 GB+ backups are done. The 3rd is backing up now.
So, TM has access to backup to the TC.
That Mac also has 'Connected Servers' checked in Finder - therefore, the TC does show up in Finder - but it has no access to connect to the TC without entering the password.
Went looking for the TC password on this 3rd Mac - Not sure where TM stores the password so that it can connect - I did go looking on that machine to see if I could discover the password after starting TM - it's not anywhere I looked, incl'g in Keychain Access.
However, for your own peace of mind, there are multiple options you can set up for privacy related to accessing the disk. Airport Utility provides setting up access/password for file sharing based on the device, the disk or by user. So, should be plenty of options there to protect the data from outside access while at the same time permitting TM access. So you could set up file sharing and add only your account with it's own password.