It's a little more than awareness. Other generations learned about separating public and personal lives when they first entered the workforce.
These days, with 13-year-olds on Facebook, they get this training a lot earlier. Not when they're 13, of course, but by the time they hit university, they know a lot about managing what us old people call "personal brand".
Of course, for them, it's stupidly obvious that they have to search for themselves and monitor what shows up. And that translates into an awareness of SEO.