Well, I will say that it IS possible that they all assumed the woman knew you were there or that someone else informed her. So, then no one told her you were there.
But if she knows she has an appt, then deduction should tell her that you're probably there. And she probably knew but as she was behind, she felt weird acknowledging you after 4 and then taking someone else back. not an excuse, but that could be what happened.
In the end, though, if you aren't comfortable with her, then use someone else. Nothing wrong with that.
However (day late and a dollar short) in this situation, at 15 mins I would have grabbed a teller / other available employee and asked to speak with Jane or a branch manager. I expect banks to run on time!
I wouldn't use her. I wouldn't even use that bank. Someone should have stepped in and helped you if there was anyone else there that could have gotten the work done. That's a really long time to wait when you had an appointment. Why bother having an appointment?
I wouldn't use her. I wouldn't use a bank at all. I think you will have an easier process and get a better deal if you use a mortgage broker. (I think you are in the US. If you are in Canada, I have no idea if this is true).