Text-boxes use a new-line character which is "\n" or "\r\n" or "\r" depending upon your operating system (unix, windows, or mac).
In order to change that to HTML line-breaks, you need to use [man]nl2br/man or do a simple search & replace, replace "\n" with '<br />'.
If you look at your pages source code, I'm sure you'll see the new-lines as well as the tabs.
As for tabs, you'd need to replace "\t" with ' ' (4 spaces).