Is it an advantage to be a resident of the state in which you are applying to PhD programs at state universities?
I had assumed that since my tuition would be covered anyways in a PhD program, there was no advantage to being in-state. 


There's no financial advantage to you.  There might be one to the department.

I believe that one common arrangement is that the department's budget is charged for the normal amount of your tuition, whether in-state or out-of-state.  Although it's just money moving between internal university accounts, it makes a difference to the department.  

I went to grad school at a University of California campus, and there was a rule that if you had come from another state, you had to establish California residency within your first year, so that the department only had to pay the out-of-state rate for one year.  So if you plan to attend a California university, you'll likely have to go through that bureaucratic hassle eventually anyway; might as well get started now.

Being in-state also means that the department gets to pay the lower rate from the beginning, so you'd be a bit cheaper to support than an out-of-state student.  I don't know whether departments actually make this an explicit factor in admissions, and I would guess that they don't, but it could make a very slight difference at the margin.