For some reason, the command line switch --kiosk
doesn't work in Mac OSX, and from what you're describing, maybe it doesn't work at all. ( http://peter.sh/experiments/chromium-command-line-switches and scroll down to --kiosk, THEN to the footnote....no explanation, but there it is).
You didn't specify if this a Mac OSX or Windows issue you're having, so I'm sorry if this doesn't help...
To workaround this on Mac OSX, you have to take two steps.
(It's still kind of wonky even then, because each new tab is a new fullscreen app at least in Lion)
Create an App pointing to your URL with this handy script.
Take note of your app's name (replace [MyAppName] below) and create the following applescript:
do shell script "open '/Applications/[MyAppName].app' "
tell application "[MyAppName]" to activate
tell application "System Events"
keystroke "f" using {command down, shift down}
end tell
Save that applescript as an application, and run it.
You can change the icon of your app as well. Here's how in case you didn't already know (like me. had to look it up): http://support.apple.com/kb/ht2493