I've had two different situations. In the classroom and as a media specialist I've had my own aide that followed my program. I've also been in buildings with individual tutors much like I think you're dealing with. They has either a special student for one-to-one support and followed them from class to class or had a period by period schedule of different students. I found that the ones with one-to-one assignments saw themselves as their student's advocate and their responsibility was only to them. The ones with a rotating schedule saw themselves as school employees with responsibility for the behavior and success of students as a whole. They acted more like teachers when faced with discipline problems.
Have you talked with the administrators, guidance or special ed department? Who hired and supervises this person? I think I'd find out more about her job description and their expectations. It sounds like she might have an attitude problem. They might not realize she's ducking responsibility by hiding out when her student is absent and not taking an active part in supporting instruction, discipline and school climate. This person might also be one of those who enjoys watching others have problems while thinking she's smarter or more observant. Pointing out the misbehaving student to you might be her way of putting you down. No matter what the problem I don't think she seems to care enough to be a helpful advocate for her student or education.
If she were in my media center doing nothing I'd ask the supervisor for permission to put her to work or to have her go elsewhere and maybe work for them during her free periods. Either let her know what you expect and have permission to hold her accountable or get her out of your way and let them see how unhelpful she is.
