An end user can only hope their password is hashed, until the site is hacked and the passwords (or, hopefully, their salted and hashed versions) are leaked to the public.
As a manager, you have a few more options. You can ask where the passwords are stored, and verify that they are not stored in plaintext.
You could take this a step further and make it part of an automated test process - create a new user, with a randomized password. Verify that the new password does not show up in the database table that stores the user authentication data. You could even go further and test if the table you look at, really is the table used for user authentication - for example, by forcibly removing the user at the database level and trying to login again.
Automated systems, unfortunately, cannot give you a 100% guarantee that passwords aren't stored in plaintext somewhere in the code.
Human process is also prone to error and overlooking things. However, the combination of good automated tests and good human process (e.g. code reviews) should give you sufficient confidence that your user's data is protected properly. Or, if the worst comes to the worst, that you at least made a serious effort to protect the data.
As Khajak Vahanyan points out in the comments, SSL/TLS has nothing to do with it. SSL/TLS is about how the data is transported to the application, not about what happens to the data afterwards.