And welcome to LQ!
I don't know Plesk (I heard the name but never saw/used it).
In the first place I think you should be asking the people who provided
you with the set-up this question.
As a rule of thumb (and good practice) server processes SHOULDN'T be
run as root, but as some other (daemon) user. That said I'd assume
that the files should be owned by that user.