The possibility of what happens here is actually temporary files that are saved. You say that video compression seems to cause this increase in space.
There are two ways to confirm this in one of two ways. Reboot the device you are testing on. Temporary elements will be cleared by the system either if additional space is needed, or when the system is turned off.
Another method (and probably more informative) is to explore the Application through the Xcode organizer. You can do this by selecting the application on the device and viewing the application directory structure. Each application receives 3 directories, / Documents, / Library and / tmp.
For intensive operations that may require large amounts of memory, some libraries will save completed data to disk to free up memory. As soon as the operation is completed, it will give you a data block, which will either refer to the data in the temporary file, or the completed data will be loaded back into the memory. This process is completely transparent to the user and the developer and uses a large amount of flash memory, and does not fully rely on relatively limited RAM.
If this is not a temporary file, but something that is in the Documents folder of the application (or even the library), it would be useful to download it to your computer and try to investigate its contents, as this may give you some hints regarding of what is happening.
Hope this helps
Edited point for clarity
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