This is fairly inconsequential, but I'm not sure how people typically count years for graduate studies. In my case, having an MA means that I have fewer years to do in the PhD program. This is physically my first year at this particular university, but would I technically say I'm a 3rd year still?
Edit: This would be at a university in the US, although in my case, my MA was done in Canada.
This does indeed seem quite inconsequential, but usually first year would imply that it's the first year you're enrolled in graduate studies at that particular institution, or even a given program. In my experience, phrases like "first year, but I came in with a masters" get used if there's a need to make that distinction.
This may also depend on your program. For example, where I did my PhD, coming in with a Masters (usually an MPH rather than an MA) didn't actually get you much of a "boost". Those that came in with Masters were in the same classes I was (I entered with a BA) and their time-until-graduation was roughly similar.
In that context, "Third Year" would imply several things about their progress in both coursework and various administrative milestones that weren't true.
