The American League playoffs will take place at National League ballparks so as to not give any of the teams involved home-field advantage. The Athletics and Rays finished with better regular-season records than their opponents, so in these best-of-five series they will bat last in Games 1, 2 and 5.
Regarding these matchups, there’s been quite a bit of bad blood between these teams, per this MLB.com article. Yankees/Rays:
Maybe it started when CC Sabathia yelled a few colorful words at the Tampa Bay dugout a couple of years ago.