I don't even have an iTunes Store account but I suspect in your case what may be happening is when you buy an item from the store it is automatically getting added to other devices from Apple's servers (something you can configure?), unless you are actually syncing with your computer's iTunes library over home wi-fi. What I know for sure is your iTunes library can only be synced over local wi-fi, not over the Internet in general unless you are running special third party software.
iTunes Store: How to enable Automatic Downloads - http://support.apple.com/kb/HT4539 - "iTunes 10.3 3 and iOS 4.3.3 or later (iOS 5 or later for iPhone (CDMA Model)) enable you to automatically download purchases from the App Store, iBookstore, or iTunes Store instantly to your other computers and devices.
"How to Use Wireless Sync in iOS 5 - http://www.pcworld.com/article/242242/how_to_use_wireless_sync_in_ios_5.html
iTunes 10.5 and later: Troubleshooting iTunes Wi-Fi Syncing - http://support.apple.com/kb/TS4062