It seems that this new feature - along with the iTunes 10.4 BETA itself - still seems to be a little "buggy" for some users. I have my own issues with file sharing and the Pages app since I updated to iTunes 10.4 and updated Pages on my Mac over the weekend.
I wish I had a solution for you on this one. I never tried this feature until just now and it works fine for me - download on iPad and it downloads in iTunes on my Mac - download in iTunes on my Mac - also downloads on iPad.
It should work like this.
This is what I do.
On the iPad - open the Pages document that you want to send to iTunes. Tap on the wrench icon in the upper right corner and a pop up window appears. Select "Share and Print". In the next window that pops up - Select "Send to iTunes". Then a window pops up letting you choose among 3 different formats - Pages, PDF and Word. Tap on the format that you want and then it "sends" the document to iTunes. The next time that you sync, click on the apps tab in iTunes, scroll down to the list of file sharing apps, click on Pages and then the document should appear in the window on the right. If you want to copy the file to your Mac desktop, click on the file in the Pages document window on the right, click on "Save To" in the lower right corner of the Pages documents window and select where you want to place the file.
To send a file the other way - computer to iPad - connect your iPad, launch iTunes, select your device on the left side, click on the apps tab, scroll down to the file sharing apps, click on Pages. Then click on "Add" in the bottom right corner of the Pages Document window, select the compatible file that you want to transfer and click open. Then open Pages on the iPad, clcik on the + sign in the upper left corner, select "Copy From iTunes", select the file from the next window that pops up and it will import into Pages.