I believe every hockey rink is designed so that each bench is "closer" to one defensive zone than the other. The team occupying that bench will defend the "closer" zone in periods 1 and 3. This is most notable when the benches are on the same side of the ice, which is common in the NHL.
A funny tidbit about our old barn, Starr Rink: one of the benches was tied into the hallway that the visiting team would cross over to reach their locker room, but that was Colgate's bench. The visiting team would have to cross over the ice to reach their bench before the start of a period (and the coaching staff would have to slowing walk across the ice to get there). The penalty boxes were adjacent to the visiting team's bench, but across the ice from Colgate's bench. When a visiting team killed a penalty, they could quickly make a substitution, but when Colgate killed a penalty, the skater would have to cross the ice if going right to the bench.
Originally Colgate occupied the bench next to the penalty boxes (and would shoot twice at the press box end of the rink), but it was flip-flopped so that the visiting bench would be right behind the student section, making it difficult for the visiting team during a late-game timeout situation.
In our new arena, this has been rectified so that each bench is tied to a tunnel for each locker room, and the Colgate bench is adjacent to the penalty boxes.