In many ways, Mark Watney is the first true Martian.
That doesn't mean that he's the first person to visit Mars. Ares 3 is—as its name implies—the third manned mission to the planet, which means that at least twelve people have already made the same fateful trek. However, those astronauts only stay on the planet for thirty days, while Mark is trapped there for nearly two years.
As you can imagine, this means that Mark has a much more intimate relationship with the planet than his peers. He travels thousands of kilometers on end. He even grows crops. That second one is important, because "once you grow crops somewhere, you have officially "colonized" it" (13.7). Everyone else simply took a vacation to Mars; Mark made it his home.
So unless there's a secret city filled with green Martians somewhere on the planet, Mark is the first individual to actually live there: he's the first Martian.