Is it expected that a part-time masters student publish before transferring to a PhD?
The expectation to publish does not depend on whether you are full-time, half-time or spare-time student, it is based on the general expectations on students in your field, department, or academic culture, or some combination. If a PhD thesis is a monograph then the main focus will be to complete such a thesis. this commonly does not preclude publishing as well. If you need to write a thesis that consists of published papers and manuscripts then that is what you need to do. 

I doubt the advisor is the key player here although that person will be representative of what you can expect from your graduate school education in terms of expectations on your writing. So check what is written in the form of PhD these and you will know. Communicating your results will inevitably be required so some form of written result will be on the horizon.