The dugout on the first base side is always home no matter what league you are in.
The home dugout is the first base dugout.
The Yankees, at home, always use the dugout on the first base side.
In baseball the home team is in the first base dugout and the visiting team is in the third base dugout. So when the Devil Rays are playing at home they are in the first base dugout. When they are playing a road game, they are in the third base dugout.
The Royals' home dugout is on the first base side.
Yes several teams do. The Red Sox dugout is and always has been on the first base side to name one.
First base line
The Jays' dugout is along the third base line at the Rogers Centre, while the opposition dugout is along the first base line.
The Mets home dugout is on the first base side.
In little league baseball, the home team dugout is the 3rd base dugout.
Because the first base side is usually the home team side. Since the Yanks are always the home team at Yankee stadium, that's where they put the dug out. :-)