Hi Matt,
Welcome to JavaRanch and this forum.
You should assume that the examiner will never run two instances of your server at the same time. Nor will they run two instances of your stand alone client at the same time. Nor will they run your server and a stand alone client at the same time.
There will only ever be
one application running that can
directly modify the database file.
There may be several clients running in client/server mode, but they will not be
directly modifying the database - they will be using the server to do all the modifications.
Regards, Andrew