I had hard time to set up ftps in Webstorm. I tried to connect to Azure server with ftps (not ftp). I could successfully do it with FileZilla. However, I couldn't so with WebStorm. So, I investigated a little bit what caused the problem. I noticed the first clue that using FTPS in "Passive Mode" in Webstorm worked just fine. I googled to find what makes "Passive Mode" different.
FTPS can run in either "Passive" or "Active". The old way, Active Mode, has some usability issue from the client-side, because when a client tries to access to a ftp server, the ftp server responds back to the client's port, which is a randomly selected port number higher than 1023. Most users (including my case) experience a trouble here, because the firewall of a user computer is likely to block the port. Hidden side is that some ftp client (like FileZilla) explicitly displays the message that the user is required to open the port with the user's own risk to make successful communication (By the way, FileZilla uses default option so that users do not worry about which they choose).
Because Active Mode is not user-friendly (firewall block), Passive Mode is introduced so that user clients can communicate with any port number higher than 1023 without any user engagement. Azure supports "Passive Mode" for ftp connection mode. This means more maintenance for ftp server admin because they have to manage more ports securely in server side. However, this choice makes users more convenient because users does not necessarily deal with firewall issue.
WebStorm does not allow me to connect to an Azure FTPS, unless I turn "Passive Mode" on.
For learning the details of how active/passive mode of FTPS work, read the summary at the bottom of this page, http://slacksite.com/other/ftp.html