Yes, Auto FTP Manager supports FTPS connections.

The authentication is defined when creating the profile, the certificate is accepted from the FTP server during connection. Create your profiles, and enter your username and password. Make sure to select FTPS from the type of connection. Choose implicit when using port 990, and use explicit when using port 21.

You will be prompted during connection if you manually run the automated transfer, the certificate is automatically accepted when the transfer runs on a schedule.