No, you are only paying once through humblebundle.com.
From the 'Download your Humble Bundle' page after choosing to download for Ubuntu:
Notes: As these games have been recently added to Ubuntu Software Center it might take a minute for them to appear. If you see a "Not found" message, Ubuntu Software Center is working in the background to update the list of available apps.
To install the app once Ubuntu Software Center has opened click on the "Buy..." button, don't worry you won't be charged for it.
Also if your bundle included Psychonauts and it does not appear here it will be available shortly, please check back soon.