No, you misunderstood it. Roundcube is to IMAP Email what OS X is to it's hardware. Essentially Roundcube is just a web GUI to read, reply, and manage your IMAP mail. You run Roundcube from a webserver. Roundcube is just a set of PHP scripts that use an IMAP connection like that of Apple Mail to connect to your IMAP server and see what's on it. RC then stores (if allowed) a few of the messages for more speedy delivery. When you "delete" an email, RC sends a command to the IMAP server and the IMAP server then either obeys because it's a valid command, or disobeys because it's invalid (or something went wrong).
Now, Apple Mail is a Desktop GUI to your IMAP mail server. So you can use both interchangeably. The difference is that Apple Mail might run faster on your Desktop since, well, it has a lot more resources to work with, and RC is just running through the browser. You just have to be careful and make sure if you do anything in Apple Mail or RC that you "update" or fetch new messages in the other application before you do anything as you might mess up and delete a wrong message.
I hope that cleared it up for you.