That might depend on their age...I remember him first as a player with the A's, for whom he was already "high profile" before his move to NY, or Anaheim, or....Baltimore!
But the then (and now?) NYC-centricity of all media, especially the sports media, certainly magnified his not inconsiderable accomplishments as a Yankee, and I suspect that that ongoing media spotlight contributes to younger fans remembering him as a Yankee. That's not unjustifiable either, since that is where he became "Mister October". But in my memory, my reflexive memory is of him as an A, because that team ws way, waaaay cool, and if you weren't around then to experience the "shock" about their looks and attitude, you'd be hard-pressed to fully understand. But I was, and I distinctly remember Reggie as a big part of them, outspoken even then, an outspoken, "Alex Johnson with real skills" type guy.