Doing something "voluntarily" means that you do it by your own choice, rather than being forced to do it. That can either mean that you wanted to do it, or that you accepted someone's request.
For example, in the situation above, if the new employee asked to move, she would say that she "moved voluntarily". But she could also say that she "moved voluntarily" if her boss offered to transfer her and let her choose whether to stay or go.
Here are some other examples of how to use "___ voluntarily":
Officials today expanded the evacuation area around Fukushima from 12 to 19 miles, urging residents to leave voluntarily.
There's been some speculation as to whether Griffin resigned voluntarily or was forced out of the company.