To update your Google Drive offline files on your Android device, you can use Wi-Fi or Mobile Network. To auto update files and folders over WiFi only, do as follows (for offline files):
1. Open "Google Drive" on your Android phone or tablet
2. Press "Menu Button" and select "Settings"
3. Tap "When to auto-update"
4. Select one of the following: Never, Over Wi-Fi only, Over Wi-Fi or mobile network