Are you using the full version of White Noise or the lite version? You can hear the standard White Noise sounds AND the alarm playing? I will look into why this happened.
Until an update is ready, you can try going into Settings > Applications > Manage Applications and choose White Noise. From there, clear the user data. Note that if you do this, your favorites, timer, alarm, and general settings will need to be reconfigured, but this should also clear the alarm state. If that doesn't work, try to reinstall the app.
Thanks for letting us know of the issue and sorry for the inconvenience.