As a tutor, you have the responsibilities that come with a paid position.
Nothing can undermine a writing center more than irresponsible tutors.
Be at work when asked, and be on time. Remain at your position until time to leave. If you must leave the center for a few minutes, leave a note specifying when you will return. You will probably do a variety of jobs in addition to tutoring. For many writing centers, documentation is critical, so the Director may ask you to fill out tutor response sheets and to file handouts.