It's definitely happening on the device. Document recognition like this moved onto the device about 3 years ago, and in fact if they didn't do this device side they would have a harder time dealing with the Mitek patents[1] that are in this space.

The actual OCR and data extraction likely occurs on the server side, but the document recognition on device is a much better user experience.

[1] USAA and Mitek were suing each other over the patents from 2012-2014.