Assuming the issue is related to permissions then you would need chmod 777 on the unsplash-stock-photo-library/admin/ directory.
https://stackoverflow.com/a/10842911/921927
The plugin is required to write a /tmp directory and then process files into the directory to prepare for upload to the media library – Once uploaded the files are then deleted from the server.
Is it a shared hosting environment? Another issue could be you php.ini is set to not allow the required functions such as file_put_contents()
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I’m away from the computer for the next couple of days, but i’ll check on this when back in town… i hope you get this sorted.