If it looks like the app consumes the battery of your device too much or the background activity seems to be concerning, here are the details you should know as well as some steps you can take in order to improve the situation.
If you have a lot of files in the app and you enable Indexing in the app's settings for the very first time, the process might take some time and drain your battery noticeably. Once all the files are indexed, the battery usage for Documents should also get back to normal.
Another process that might influence both the battery usage and the background activity is the initial sync (the very first time you establish sync with a cloud storage) - it also consumes additional resources, but once it's done, everything should be working correctly.
The steps you can take to troubleshoot the problem are as follows:
If the issue persists after these steps, please provide us with screenshots from your iOS Settings > Battery at firstname.lastname@example.org - also, please try to trace your actions with the app when the problem happens.