What they do is download a little database (list) of those hashes to your iPhone (this list gets updated regularly), then when uploading a file to iCloud they simply compute the hash/checksum and compare it to the list.
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Yup it's here in their FAQ, it's very clearly explained here how it works:
apple.com/child-safety/pdf/Expande...
What they do is download a little database (list) of those hashes to your iPhone (this list gets updated regularly), then when uploading a file to iCloud they simply compute the hash/checksum and compare it to the list.